Monoobjective resolution

 # Prerequisites
 *.d
 
+# LaTeX temporary files
+doc/*.toc
+doc/*.bbl
+doc/*.gz
+
 # Compiled Object files
 *.slo
 *.lo

+# Please set the following variables to the correct paths for JAR3D:
+jar3dexec="/home/persalteas/Software/jar3dbin/jar3d_2014-12-11.jar"
+ILmotifDir="/home/persalteas/Data/RNA/motifs/Matlab_results/IL/3.2/lib"
+HLmotifDir="/home/persalteas/Data/RNA/motifs/Matlab_results/HL/3.2/lib"
\ No newline at end of file

-# ------------------------------------------------
-# Generic Makefile
-# ------------------------------------------------
+ICONCERT=/opt/ibm/ILOG/CPLEX_Studio_Community128/concert/include
+ICPLEX=/opt/ibm/ILOG/CPLEX_Studio_Community128/cplex/include
+LCONCERT=/opt/ibm/ILOG/CPLEX_Studio_Community128/concert/lib/x86-64_linux/static_pic/
+LCPLEX=/opt/ibm/ILOG/CPLEX_Studio_Community128/cplex/lib/x86-64_linux/static_pic/
 
 # project name (generate executable with this name)
-TARGET   = motifscan
+TARGET   = biominserter
 
 CC	   = g++
 # compiling flags here
-CFLAGS   = -I. -O3
-CXXFLAGS = -std=c++17 -Wall -Wpedantic -Wextra
+CFLAGS   = -Icppsrc/ -I$(ICONCERT) -I$(ICPLEX) -O3
+CXXFLAGS = -std=c++17 -Wall -Wpedantic -Wextra -Wno-ignored-attributes
 
 LINKER   = g++
 # linking flags here
-LDFLAGS   = -lboost_system -lboost_filesystem -lboost_program_options
+LDFLAGS   = -lconcert -lilocplex -lcplex -lm -lpthread -ldl -lboost_system -lboost_filesystem -lboost_program_options -L$(LCONCERT) -L$(LCPLEX)
 
 # change these to proper directories where each file should be
-SRCDIR   = src
+SRCDIR   = cppsrc
 OBJDIR   = obj
 BINDIR   = bin
 

-# RNA_Motifs_Inserter
-A C++ software interface to RNA motif databases, and algorithms to include known motifs in raw sequences.
+This is a bi-objective integer programming algorithm.
+It predicts the secondary structure of a RNA sequence with pieces of 3D information (non-canonical contacts) at some places, 
+by identifying zones that can fold like known motifs.
+
+1/ How it works
+===================================
+INPUT:
+- An RNA sequence (tested with sequences ~100 bases)
+
+THEN
+- Identifies possible 2D folds with RNAsubopt.
+- Knowing possible 2D folds, locate every possibly unpaired loop (hairpin loop, internal loop, multiple junction...)
+- align each unpaired loop to the catalogue of models of known RNA motifs (The 3D Motif Atlas of the BGSU RNA group)
+- retrieve a list of potential motif-insertion-sites in the RNA sequence. Use them to define the constraints for the IP problem.
+- Solve a bi-objective IP problem: 
+    * Maximize the expected accuracy of the secondary structure,
+    * Maximize the number and size of motifs inserted in the structure.
+
+OUTPUT:
+- A set of secondary structures from the pareto front,
+- The list of known motif inserted in the corresponding structures (and the non-canonical contacts)
+- (Optionally, lower score structures from k-Pareto sets.)
+
+2/ Installation
+==================================
+- Download and install RNAsubopt from the ViennaRNA package (https://www.tbi.univie.ac.at/RNA/)
+- Download and install IBM ILOG Cplex optimization studio (https://www.ibm.com/analytics/cplex-optimizer), free academic account required
+- Download and install Java runtime (Tested with Java 10)
+- Download and install the latest JAR3D executable "jar3d_releasedate.jar" and motif models in this folder (http://rna.bgsu.edu/data/jar3d/models/)
+  Note that for HL and ILs, only the latest version is required (not all the versions provided in the folders).
+- Download and install a C++ compiler and building dependencies and utilities (g++ or clang, automake, libboost)

+#include "MOIP.h"
+#include "SecondaryStructure.h"
+#include "rna.h"
+#include <algorithm>
+#include <boost/format.hpp>
+#include <cfloat>
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+#include <limits>
+#include <stdexcept>
+#include <utility>
+#include <vector>
+
+using std::cerr, std::cout, std::endl;
+using std::make_pair;
+using std::vector;
+
+uint MOIP::ncores = 0;
+
+MOIP::MOIP(const RNA& rna, const vector<Motif>& insertionSites)
+: rna_(rna), insertion_sites_(insertionSites), beta_(1.0), theta_{1.0 / (2.0 + 1.0)}
+{
+    basepair_dv_  = IloNumVarArray(env_);
+    insertion_dv_ = IloNumVarArray(env_);
+
+    // Add the y^u_v decision variables
+    uint u, v, c = 0;
+    index_of_yuv_ = vector<vector<size_t>>(rna_.get_RNA_length() - 6, vector<size_t>(0));
+    for (u = 0; u < rna_.get_RNA_length() - 6; u++) {
+        for (v = u + 4; v < rna_.get_RNA_length(); v++)    // A basepair is possible iff v > u+3
+        {
+            index_of_yuv_[u].push_back(c);
+            c++;
+            char name[15];
+            sprintf(name, "y%d,%d", u, v);
+            basepair_dv_.add(IloNumVar(env_, 0, 1, IloNumVar::Bool, name));    // A boolean whether u and v are paired
+        }
+    }
+    // Add the Cx,i,p decision variables
+    index_of_first_components.reserve(insertionSites.size());
+    index_of_Cxip_ = vector<vector<size_t>>(0);
+    index_of_Cxip_.reserve(insertionSites.size());
+    size_t i = 0;
+    for (const Motif m : insertionSites) {
+        index_of_first_components.push_back(i);
+        index_of_Cxip_.push_back(vector<size_t>(0));
+        for (const Component c : m.comp) {
+            index_of_Cxip_.back().push_back(i);
+            if (c.k > 0) i++;
+            char name[20];
+            sprintf(
+            name,
+            "C%d,%d-%d",
+            static_cast<int>(index_of_Cxip_.size() - 1),
+            static_cast<int>(index_of_Cxip_.back().size() - 1),
+            c.pos.first);
+            insertion_dv_.add(IloNumVar(env_, 0, 1, IloNumVar::Bool, name));    // A boolean whether component i of motif x is inserted at position p
+        }
+    }
+    cout << i + c << " decision variables are used !" << endl;
+}
+
+
+MOIP::~MOIP() { env_.end(); }
+
+
+bool MOIP::is_undominated_yet(const SecondaryStructure& s)
+{
+    for (uint i = 0; i < pareto_.size(); i++) {
+        if (pareto_[i] > s) return false;
+    }
+    return true;
+}
+
+void MOIP::solve_objective(int o, double min, double max)
+{
+    IloModel model_ = IloModel(env_);
+    cout << "Solving objective function " << o << "..." << endl;
+    add_problem_constraints(model_);
+    switch (o) {
+    case 1: {
+        // Add the motif objective function
+        IloExpr obj1 = IloExpr(env_);
+        for (uint i = 0; i < insertion_sites_.size(); i++) {
+            IloNum n_compo_squared = IloNum(insertion_sites_[i].comp.size() * insertion_sites_[i].comp.size());
+            obj1 += n_compo_squared * insertion_dv_[index_of_first_components[i]];
+        }
+        model_.add(IloMinimize(env_, obj1));
+    } break;
+    case 2: {
+        // Add the likelihood objective function
+    }
+    }
+    IloCplex cplex_ = IloCplex(model_);
+    if (!cplex_.solve()) {
+        env_.error() << "\t>Failed to optimize LP." << endl;
+        throw(-1);
+    }
+    IloNumArray basepair_values(env_);
+    IloNumArray insertion_values(env_);
+    env_.out() << endl << "Solution status = " << cplex_.getStatus() << endl;
+    env_.out() << endl << "Objective value = " << cplex_.getObjValue() << endl;
+    cplex_.getValues(basepair_values, basepair_dv_);
+    env_.out() << endl << "Basepair Values = " << basepair_values << endl;
+    cplex_.getValues(insertion_values, basepair_dv_);
+    env_.out() << endl << "Insertion Values = " << insertion_values << endl;
+
+    // TODO : retrieve the secondary structure !!
+}
+
+void MOIP::add_problem_constraints(const IloModel& model_)
+{
+    // ensure there only is 0 or 1 pairing by nucleotide:
+    cout << "\t>ensuring there are 0 or 1 pairing by nucleotide..." << endl;
+    uint u, v;
+    uint n = rna_.get_RNA_length();
+    for (u = 0; u < n - 6; u++) {
+        IloExpr c1(env_);
+        for (v = 0; v < u; v++)
+            if (allowed_basepair(v, u)) c1 += y(v, u);
+        for (v = u + 4; v < n; v++)
+            if (allowed_basepair(u, v)) c1 += y(u, v);
+        model_.add(c1 <= 1);
+        // cout << "\t>It worked for base " << u << " : " << (c1 <= 1) << endl;
+    }
+    // forbid lonely basepairs
+    cout << "\t>forbidding lonely basepairs..." << endl;
+    for (u = 0; u < n - 6; u++) {
+        IloExpr c2(env_);    // for the case where s[u] is paired to s[v], v>u
+        c2 += 1;
+        for (v = u; v < n; v++)
+            if (allowed_basepair(u - 1, v)) c2 += y(u - 1, v);
+        for (v = u + 1; v < n; v++)
+            if (allowed_basepair(u, v)) c2 -= y(u, v);
+        for (v = u + 2; v < n; v++)
+            if (allowed_basepair(u + 1, v)) c2 += y(u + 1, v);
+        model_.add(c2 >= 1);
+        // cout << "\t>It worked for base " << u << " : " << (c2 >= 1) << endl;
+    }
+    for (v = 5; v < n; v++) {
+        IloExpr c2p(env_);    // for the case where s[u] is paired to s[v], v<u
+        c2p += 1;
+        for (u = 1; u <= v - 2; u++)
+            if (allowed_basepair(u, v - 1)) c2p += y(u, v - 1);
+        for (u = 1; u <= v - 1; u++)
+            if (allowed_basepair(u, v)) c2p -= y(u, v);
+        for (u = 1; u <= v; u++)
+            if (allowed_basepair(u, v + 1)) c2p += y(u, v + 1);
+        model_.add(c2p >= 1);
+        // cout << "\t>It worked for base " << u << " : " << (c2p >= 1) << endl;
+    }
+    // Forbid pairings inside every motif component if included
+    cout << "\t>forbidding basepairs inside included motif's components..." << endl;
+    for (size_t i = 0; i < insertion_sites_.size(); i++) {
+        Motif& x = insertion_sites_[i];
+        for (size_t j = 0; j < x.comp.size(); j++) {
+            Component& c = x.comp[j];
+            IloExpr    c3(env_);
+            IloNum     kxi = IloNum(c.k);
+            c3 += kxi * C(i, j);
+            for (u = c.pos.first; u < c.pos.second; u++) {
+                for (v = 0; v < n; v++)
+                    if (allowed_basepair(u, v)) c3 += y(u, v);
+            }
+            model_.add(c3 <= kxi);
+        }
+    }
+    // To be continued ...
+}
+
+void MOIP::extend_pareto(double lambdaMin, double lambdaMax)
+{
+    if (lambdaMin >= lambdaMax) {
+        cerr << "lambdaMax < lambdaMin, something's wrong !" << endl;
+        exit(EXIT_FAILURE);
+    }
+
+    // for any SecondaryStructure in pareto_ such that the value of the second
+    // objective is between lambdaMin and lambdaMax
+    // a DIFF() constraint and a mirror constraint is added
+    for (uint i = 0; i < pareto_.size(); i++) {
+        // DIFF()
+        if (
+        (abs(pareto_[i].get_objective_score(2) - lambdaMin) < PRECISION or pareto_[i].get_objective_score(2) > lambdaMin) and
+        (abs(pareto_[i].get_objective_score(2) - lambdaMax) < PRECISION or pareto_[i].get_objective_score(2) < lambdaMax)) {
+            // ip.add_bj_ct(pareto_[i]);
+        }
+        // mirror
+        // if (
+        // (abs(pareto_[i].get_obj2M_() - lambdaMin) < PRECISION or pareto_[i].get_obj2M_() > lambdaMin) and
+        // (abs(pareto_[i].get_obj2M_() - lambdaMax) < PRECISION or pareto_[i].get_obj2M_() < lambdaMax)) {
+        //     ip.add_bj_ct_M(pareto_[i]);
+        // }
+    }
+
+    // SecondaryStructure s = solve_objective(1, lambdaMin, lambdaMax);
+
+    // if (is_undominated_yet(s)) {
+    //     // adding the SecondaryStructure s to the set pareto_
+    //     add_solution(s);
+    //     // run localPareto above the SecondaryStructure s
+    //     extend_pareto(s.get_objective_score(2), lambdaMax);
+    // }
+}
+
+size_t MOIP::get_yuv_index(size_t u, size_t v) const
+{
+    size_t a, b;
+    a = (u < v) ? u : v;
+    b = (u > v) ? u : v;
+    return index_of_yuv_[a][b - 4 - a];
+}
+
+size_t MOIP::get_Cpxi_index(size_t x_i, size_t i_on_j) const { return index_of_Cxip_[x_i][i_on_j]; }
+
+
+bool MOIP::allowed_basepair(size_t u, size_t v) const
+{
+    size_t a, b;
+    a = (v > u) ? u : v;
+    b = (v > u) ? v : u;
+    if (b - a < 4) return false;
+    if (a >= rna_.get_RNA_length() - 6) return false;
+    if (b >= rna_.get_RNA_length()) return false;
+    return true;
+}
\ No newline at end of file

+#ifndef MOIP_H_
+#define MOIP_H_
+
+#define IL_STD
+
+#include "SecondaryStructure.h"
+#include "rna.h"
+#include <ilcplex/ilocplex.h>
+
+using std::vector;
+
+const double PRECISION = 0.0001;
+
+
+class MOIP
+{
+  public:
+    static uint ncores;
+    typedef enum { MIN, MAX } DirType;
+    typedef enum { FR, LO, UP, DB, FX } BoundType;
+    MOIP(const RNA& rna, const vector<Motif>& motifSites);
+    ~MOIP(void);
+    void                      solve_objective(int o, double min, double max);
+    uint                      get_n_solutions(void) const;
+    const SecondaryStructure& solution(uint i) const;
+    void                      extend_pareto(double lambdaMin, double lambdaMax);
+    bool                      allowed_basepair(size_t u, size_t v) const;
+    void                      add_solution(const SecondaryStructure& s);
+
+  private:
+    bool           is_undominated_yet(const SecondaryStructure& s);
+    void           add_problem_constraints(const IloModel& model_);
+    size_t         get_yuv_index(size_t u, size_t v) const;
+    size_t         get_Cpxi_index(size_t x_i, size_t i_on_j) const;
+    IloNumExprArg& y(size_t u, size_t v);    // Direct reference to y^u_v in basepair_dv_
+    IloNumExprArg& C(size_t x, size_t i);    // Direct reference to C_p^xi in insertion_dv_
+
+
+    RNA                        rna_;                // RNA object
+    vector<Motif>              insertion_sites_;    // Potential Motif insertion sites
+    const float                beta_;               // beta parameter of the probability function
+    double                     lambdaMin_;          // minimum threshold value for the probability value
+    double                     lambdaMax_;          // maximum threshold value for the probability value
+    int                        vp_;                 // vp_ variable for penalization of the probability score
+    float                      theta_;              // theta parameter for the probability function
+    IloEnv                     env_;                // environment CPLEX object
+    IloNumVarArray             basepair_dv_;        // Decision variables
+    IloNumVarArray             insertion_dv_;       // Decision variables
+    vector<SecondaryStructure> pareto_;             // Vector of results
+    vector<vector<size_t>>     index_of_Cxip_;      // Stores the indexes of the Cxip in insertion_dv_
+    vector<vector<size_t>>     index_of_yuv_;    // Stores the indexes of the y^u_v in basepair_dv_ in a complex way. Use get_yuv_index(u,v) to retrieve.
+    vector<size_t>             index_of_first_components;    // Stores the indexes of Cx1p in insertion_dv_
+};
+
+inline void                      MOIP::add_solution(const SecondaryStructure& s) { pareto_.push_back(s); }
+inline uint                      MOIP::get_n_solutions(void) const { return pareto_.size(); }
+inline const SecondaryStructure& MOIP::solution(uint i) const { return pareto_[i]; }
+inline IloNumExprArg&            MOIP::y(size_t u, size_t v) { return basepair_dv_[get_yuv_index(u, v)]; }
+inline IloNumExprArg&            MOIP::C(size_t x, size_t i) { return insertion_dv_[get_Cpxi_index(x, i)]; }
+
+#endif    // MOIP_H_
\ No newline at end of file

+#include "SecondaryStructure.h"
+#include <boost/format.hpp>
+
+static const double PRECISION(0.0001);
+
+SecondaryStructure::SecondaryStructure(const vector<double>& scores, const vector<bool>& decision_variables, VII coord, int RNAlength)
+: objective_scores_(scores), dv_(decision_variables), coord_(coord), n_(RNAlength)
+{
+}
+
+string SecondaryStructure::to_DBN(void) const
+{
+    string res(n_, '.');
+    for (size_t i = 0; i < n_; i++) {
+        if (dv_[i]) {
+            res[coord_[i].first]  = '(';
+            res[coord_[i].second] = ')';
+        }
+    }
+    return res;
+}
+
+string SecondaryStructure::to_string(void) const
+{
+    return to_DBN() + "\t" + boost::str(boost::format("%.6f") % objective_scores_[0]) + "\t" +
+           boost::str(boost::format("%.6f") % objective_scores_[1]);
+}
+
+bool operator>(const SecondaryStructure& s1, const SecondaryStructure& s2)
+{
+    double s11 = s1.get_objective_score(0);
+    double s12 = s1.get_objective_score(1);
+    double s21 = s2.get_objective_score(0);
+    double s22 = s2.get_objective_score(1);
+
+    bool obj1 = false, obj2 = false, strict1 = false, strict2 = false;
+
+    if (s11 > s21) {
+        strict1 = true;
+        obj1    = true;
+    } else if (abs(s11 - s21) < PRECISION) {
+        obj1 = true;
+    }
+    if (s12 > s22) {
+        strict2 = true;
+        obj2    = true;
+    } else if (abs(s12 - s22) < PRECISION) {
+        obj2 = true;
+    }
+
+    if (obj1 && obj2 && (strict1 || strict2)) {
+        return true;
+    }
+
+    return false;
+}
+
+bool operator<(const SecondaryStructure& s1, const SecondaryStructure& s2)
+{
+    double s11 = s1.get_objective_score(0);
+    double s12 = s1.get_objective_score(1);
+    double s21 = s2.get_objective_score(0);
+    double s22 = s2.get_objective_score(1);
+
+    bool obj1 = false, obj2 = false, strict1 = false, strict2 = false;
+
+    if (s11 < s21) {
+        strict1 = true;
+        obj1    = true;
+    } else if (abs(s11 - s21) < PRECISION) {
+        obj1 = true;
+    }
+    if (s12 < s22) {
+        strict2 = true;
+        obj2    = true;
+    } else if (abs(s12 - s22) < PRECISION) {
+        obj2 = true;
+    }
+
+    if (obj1 && obj2 && (strict1 || strict2)) {
+        return true;
+    }
+    return false;
+}

+#ifndef __INC_IP_SOL__
+#define __INC_IP_SOL__
+
+#include "rna.h"
+#include <string>
+#include <vector>
+
+using std::string;
+using std::vector;
+
+typedef vector<int>                 VI;
+typedef vector<VI>                  VVI;
+typedef vector<std::pair<int, int>> VII;
+
+
+class SecondaryStructure
+{
+  public:
+    SecondaryStructure(void);
+    SecondaryStructure(const vector<double>& scores, const vector<bool>& decision_variables, VII coord, int RNAlength);
+
+    double              get_objective_score(int i) const;
+    const vector<bool>& get_decision_variables() const;
+    bool                get_decision_value(int i) const;
+    VII                 get_coord() const;
+    int                 get_RNA_length() const;
+
+    void   set_objective_score(int i, double s);
+    string to_DBN() const;
+    string to_string() const;
+
+  private:
+    vector<double> objective_scores_;    // values of the different objective functions for that SecondaryStructure
+    vector<bool>   dv_;                  // values of the decision variable of the integer program
+    vector<Motif>  motif_info_;    // information about known motives in this secondary structure and their positions
+    VII            coord_;         // coordinates of the dv_. dv_[i] == true <==> coord_[i][0] paired to coord_[i][1];
+    size_t         n_;             // length of the RNA
+};
+
+// return if this SecondaryStructure s1 dominates s2
+bool operator>(const SecondaryStructure& s1, const SecondaryStructure& s2);
+// return if this SecondaryStructure s2 dominates s1
+bool operator<(const SecondaryStructure& s1, const SecondaryStructure& s2);
+
+inline double              SecondaryStructure::get_objective_score(int i) const { return objective_scores_[i]; }
+inline const vector<bool>& SecondaryStructure::get_decision_variables() const { return dv_; }
+inline void                SecondaryStructure::set_objective_score(int i, double s) { objective_scores_[i - 1] = s; }
+inline VII                 SecondaryStructure::get_coord() const { return coord_; }
+inline int                 SecondaryStructure::get_RNA_length() const { return n_; }
+inline bool                SecondaryStructure::get_decision_value(int i) const { return dv_[i]; }
+
+#endif

+/***
+        Biominserter
+        Louis Becquey, starting from Audrey Legendre's code
+        nov 2018
+***/
+
+#include <algorithm>
+#include <boost/algorithm/string.hpp>
+#include <cstdlib>
+#include <iostream>
+#include <iterator>
+#include <string>
+#include <thread>
+#include <vector>
+
+#include "MOIP.h"
+#include "fa.h"
+#include "nupack.h"
+
+using namespace std;
+
+Motif parse_csv_line(string line)
+{
+    vector<string> tokens;
+    boost::split(tokens, line, boost::is_any_of(","));
+    Motif m;
+    m.atlas_id = tokens[0];
+    m.comp.push_back(Component(make_pair<int, int>(stoi(tokens[3]), stoi(tokens[4])), stoi(tokens[2])));
+    if (tokens[5] != "-")
+        m.comp.push_back(Component(make_pair<int, int>(stoi(tokens[5]), stoi(tokens[6])), stoi(tokens[2])));
+    m.reversed = (tokens[1] == "True");
+    return m;
+}
+
+int main(int argc, char* argv[])
+{
+    // float   time;
+    // clock_t t1, t2;
+    // t1 = clock();
+
+    MOIP::ncores = thread::hardware_concurrency() - 1;
+
+    if (argc != 3) {
+        cerr << argc << " arguments specified !" << endl;
+        cerr << "Please specify the following input files:" << endl;
+        cerr << "biominserter sequence.fasta insertion.sites.csv" << endl;
+        return EXIT_FAILURE;
+    }
+
+
+    const char* inputName = argv[1];
+    const char* csvname   = argv[2];
+    cout << "Reading input files..." << endl;
+    if (access(inputName, F_OK) == -1) {
+        cerr << inputName << " not found" << endl;
+        return EXIT_FAILURE;
+    }
+    if (access(csvname, F_OK) == -1) {
+        cerr << csvname << " not found" << endl;
+        return EXIT_FAILURE;
+    }
+
+    // load fasta file
+    list<Fasta> f;
+    Fasta::load(f, inputName);
+    list<Fasta>::iterator fa = f.begin();
+    cout << "loading " << fa->name() << "..." << endl;
+    RNA myRNA = RNA(fa->name(), fa->seq());
+    cout << "\t>" << inputName << " successfuly loaded" << endl;
+
+    // load CSV file
+    string   line;
+    ifstream motifs = ifstream(csvname);
+    getline(motifs, line);    // skip header
+    vector<Motif> posInsertionSites;
+    while (getline(motifs, line)) {
+        posInsertionSites.push_back(parse_csv_line(line));
+    }
+    cout << "\t>" << csvname << " successfuly loaded" << endl;
+
+    // creating the Multi-Objective problem:
+    MOIP myMOIP = MOIP(myRNA, posInsertionSites);    // using the constructor with arguments automatically defines the decision variables.
+
+    // finding the best SecondaryStructures for each objective
+    double max = myRNA.get_RNA_length();
+    try {
+        myMOIP.solve_objective(1, -max, max);
+    } catch (IloCplex::Exception& e) {
+        cerr << e << endl;
+    }
+    // SecondaryStructure bestSSO1 = myMOIP.solve_objective(1, -max, max);
+    // SecondaryStructure bestSSO2 = myMOIP.solve_objective(2, -max, max);
+    // double             bestObj2 = bestSSO2.get_objective_score(2);
+
+    // extend to the whole pareto set
+    // myMOIP.add_solution(bestSSO1);
+    // myMOIP.extend_pareto(bestObj2, max);
+
+    // print the pareto set
+    // cout << "Structure \t Free energy score \t Expected accuracy score" << endl;
+    // for (uint i = 0; i < myMOIP.get_n_solutions(); i++) {
+    //     cout << myMOIP.solution(i).to_string() << endl;
+    // }
+    // cout << endl;
+
+    return EXIT_SUCCESS;
+}

+/*
+ * $Id$
+ *
+ * Copyright (C) 2010 Kengo Sato
+ *
+ * doublehis file comes from IPknot.
+ *
+ */
+
+#ifndef __INC_DP_TABLE_H__
+#define __INC_DP_TABLE_H__
+
+class DPtable2
+{
+  public:
+    DPtable2() : V_(), N_(0) {}
+    void resize(int n)
+    {
+        N_ = n;
+        V_.resize(N_ * (N_ + 1) / 2 + (N_ + 1));
+    }
+    void          fill(const double& v) { std::fill(V_.begin(), V_.end(), v); }
+    double&       operator()(int i, int j) { return V_[index(i, j)]; }
+    const double& operator()(int i, int j) const { return V_[index(i, j)]; }
+
+  private:
+    int index(int i, int j) const
+    {
+        assert(j <= N_);
+        return j == i - 1 ? N_ * (N_ + 1) / 2 + i : i * N_ + j - i * (1 + i) / 2;
+    }
+    std::vector<double> V_;
+    int                 N_;
+};
+
+class DPtable4
+{
+  public:
+    DPtable4() : V_(), N_(0) {}
+    void resize(int n)
+    {
+        N_ = n;
+        V_.resize(N_ * (N_ - 1) * (N_ - 2) * (N_ - 3) / 2 / 3 / 4);
+    }
+    void          fill(const double& v) { std::fill(V_.begin(), V_.end(), v); }
+    double&       operator()(int i, int d, int e, int j) { return V_[index(i, d, e, j)]; }
+    const double& operator()(int i, int d, int e, int j) const { return V_[index(i, d, e, j)]; }
+
+  private:
+    int index(int h, int r, int m, int s) const
+    {
+        int n  = N_;
+        int h2 = h * h;
+        int h3 = h2 * h;
+        int h4 = h3 * h;
+        int m2 = m * m;
+        int n2 = n * n;
+        int n3 = n2 * n;
+        int r2 = r * r;
+        int r3 = r2 * r;
+        assert(h <= r);
+        assert(r <= m);
+        assert(m <= s);
+        assert(s <= N_);
+        return (h == r && m == s) ? V_.size() - 1 :
+                                    (
+                                    -24 - 50 * h - 35 * h2 - 10 * h3 - h4 - 36 * m - 12 * m2 + 12 * n + 70 * h * n +
+                                    30 * h2 * n + 4 * h3 * n + 24 * m * n - 12 * n2 - 30 * h * n2 - 6 * h2 * n2 + 4 * h * n3 +
+                                    44 * r - 48 * n * r + 12 * n2 * r + 24 * r2 - 12 * n * r2 + 4 * r3 + 24 * s) /
+                                    24;
+    }
+    std::vector<double> V_;
+    int                 N_;
+};
+
+class DPtableX
+{
+  public:
+    DPtableX() : V_(), N_(0), D_(0) {}
+    void resize(int d, int n)
+    {
+        N_         = n;
+        D_         = d;
+        int max_sz = 0;
+        for (int i = d; i < d + 3; ++i) max_sz = std::max(max_sz, (N_ - i) * (i - 5) * (i - 1) * (i - 2) / 2);
+        V_.resize(max_sz);
+    }
+    void          fill(const double& v) { std::fill(V_.begin(), V_.end(), v); }
+    double&       operator()(int i, int d, int e, int s) { return V_[index(i, d, e, s)]; }
+    const double& operator()(int i, int d, int e, int s) const { return V_[index(i, d, e, s)]; }
+    void          swap(DPtableX& x)
+    {
+        std::swap(V_, x.V_);
+        std::swap(N_, x.N_);
+        std::swap(D_, x.D_);
+    }
+
+  private:
+    int index(int i, int h1, int m1, int s) const
+    {
+        int d      = D_;
+        int d1d2   = (d - 1) * (d - 2);
+        int d5     = d - 5;
+        int h1_i_1 = h1 - i - 1;
+        assert(i + d < N_);
+        assert(d - 6 >= s);
+        assert(i < h1);
+        return i * d5 * d1d2 / 2 + s * d1d2 / 2 + h1_i_1 * (d - 1) - h1_i_1 * (h1 - i) / 2 + m1 - h1 - 1;
+    }
+
+    std::vector<double> V_;
+    int                 N_;
+    int                 D_;
+};
+
+#endif

+/*
+ * $Id$
+ *
+ * Copyright (C) 2008-2010 Kengo Sato
+ *
+ * This file comes from Ipknot.
+ */
+
+
+#include "fa.h"
+#include <iostream>
+#include <fstream>
+#include <sstream>
+#include <string>
+#include <cctype>
+#include <cstring>
+#include <cassert>
+
+typedef unsigned int uint;
+
+//static
+unsigned int Fasta::load(std::list<Fasta>& data, const char* file){
+
+  std::string line, name, seq, str;
+  std::ifstream ifs(file);
+  while (std::getline(ifs, line)) {
+    if (line[0]=='>') {         // header
+      if (!name.empty()) {
+        assert(str.size()==0 || seq.size()==str.size());
+        data.push_back(Fasta(name, seq, str));
+      }
+
+      name=line.substr(1);
+      seq.clear();
+      str.clear();
+      continue;
+    } 
+
+    if (std::strchr("()[].?xle ", line[0])==NULL) { // seq
+      uint i;
+      for (i=0; i!=line.size(); ++i)
+        if (!isalpha(line[i])) break;
+      seq+=line.substr(0, i);
+    } else {
+      uint i;
+      for (i=0; i!=line.size(); ++i)
+        if (std::strchr("()[].?xle ", line[i])==NULL) break;
+      str+=line.substr(0, i);
+    }
+  }
+  
+  if (!name.empty()) 
+    data.push_back(Fasta(name, seq, str));
+
+  return data.size();
+}
+

+/*
+ * $Id$
+ *
+ * Copyright (C) 2008-2010 Kengo Sato
+ *
+ * This file comes from Ipknot.
+*/
+
+#include <list>
+#include <string>
+
+using std::list;
+using std::string;
+
+class Fasta
+{
+  public:
+    Fasta() : name_(), seq_(), str_() {}
+    Fasta(const string& name, const string& seq, const string& str = "") : name_(name), seq_(seq), str_(str) {}
+    Fasta(const Fasta& fa) : name_(fa.name_), seq_(fa.seq_), str_(fa.str_) {}
+    Fasta& operator=(const Fasta& fa)
+    {
+        if (this != &fa) {
+            name_ = fa.name_;
+            seq_  = fa.seq_;
+            str_  = fa.str_;
+        }
+        return *this;
+    }
+    const string& name() const { return name_; }
+    const string& seq() const { return seq_; }
+    string&       seq() { return seq_; }
+    const string& str() const { return str_; }
+    unsigned int  size() const { return seq_.size(); }
+
+    static unsigned int load(list<Fasta>& data, const char* file);
+
+  private:
+    string name_;
+    string seq_;
+    string str_;
+};

+#include "nupack.h"
+#include "rna1995.h"
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <fstream>
+#include <iostream>
+#include <sstream>
+
+enum { PAIR_AU = 0, PAIR_CG, PAIR_GC, PAIR_UA, PAIR_GU, PAIR_UG };
+enum { BASE_N = 0, BASE_A, BASE_C, BASE_G, BASE_U };
+enum { A = BASE_A - 1, C = BASE_C - 1, G = BASE_G - 1, U = BASE_U - 1 };
+enum { AU = PAIR_AU, CG = PAIR_CG, GC = PAIR_GC, UA = PAIR_UA, GU = PAIR_GU, UG = PAIR_UG };
+
+#define EXP expl
+#define LOG logl
+
+
+Nupack::Nupack()
+: base_map('z' - 'a' + 1), pair_map(boost::extents[5][5]), RT(kB * (ZERO_C_IN_KELVIN + 37)), salt_correction(0),
+  loop_greater30(1.079 /*=1.75*RT*/), hairpin_GGG(0.0)
+{
+    std::fill(base_map.begin(), base_map.end(), (int)BASE_N);
+    base_map['a' - 'a'] = BASE_A;
+    base_map['c' - 'a'] = BASE_C;
+    base_map['g' - 'a'] = BASE_G;
+    base_map['u' - 'a'] = BASE_U;
+    base_map['t' - 'a'] = BASE_U;
+
+    std::fill(pair_map.data(), pair_map.data() + pair_map.num_elements(), -1);
+    pair_map[BASE_A][BASE_U] = PAIR_AU;
+    pair_map[BASE_U][BASE_A] = PAIR_UA;
+    pair_map[BASE_C][BASE_G] = PAIR_CG;
+    pair_map[BASE_G][BASE_C] = PAIR_GC;
+    pair_map[BASE_G][BASE_U] = PAIR_GU;
+    pair_map[BASE_U][BASE_G] = PAIR_UG;
+}
+
+int Nupack::base(char x) const
+{
+    if (x >= 'a' && x <= 'z')
+        return base_map[x - 'a'];
+    else if (x >= 'A' && x <= 'Z')
+        return base_map[x - 'A'];
+    else
+        return BASE_N;
+}
+
+int Nupack::pair_type(int i, int j) const { return pair_map[seq[i]][seq[j]]; }
+
+int Nupack::pair_type(int i) const
+{
+    // assume Watson-Crick pairs
+    switch (seq[i]) {
+    case BASE_A: return PAIR_AU; break;
+    case BASE_C: return PAIR_CG; break;
+    case BASE_G: return PAIR_GC; break;
+    case BASE_U: return PAIR_UA; break;
+    }
+    return -1;
+}
+
+bool Nupack::wc_pair(int i, int j) const { return pair_type(i, j) != PAIR_GU && pair_type(i, j) != PAIR_UG; }
+
+bool Nupack::allow_paired(int i, int j) const { return j - i - 1 >= 3 && pair_type(i, j) >= 0; }
+
+void Nupack::load_sequence(const string& s)
+{
+    N = s.size();
+    seq.resize(N);
+    for (int i = 0; i != N; ++i) seq[i] = base(s[i]);
+}
+
+int check_stability_and_size(int k, int l, int o, int p)
+// helper function, to detect which delta we need for the int22 parameters
+{
+    // having at least one AC mismatch is the simplest, test first
+    if ((k == A && l == C) || (k == C && l == A) || (o == A && p == C) || (o == C && p == A)) return 4;
+
+    // combination of all mismatches of equal size (purine-purine, purine-pyrimidine, and pyrimidine-pyrimidine are
+    // different sizes) purine =  A, G pyrimidine = C, U if all purine-purines
+    if ((k == A || k == G) && (l == A || l == G) && (o == A || o == G) && (p == A || p == G)) return 1;
+    // if all pyrimidine-pyrimidine
+    if ((k == C || k == U) && (l == C || l == U) && (o == C || o == U) && (p == C || p == U)) return 1;
+    // if both  purine-pyrimidine
+    // assume the A-C pairs have been found above
+    if (
+    (((k == A || k == G) && (l == C || l == U)) || ((k == C || k == U) && (l == A || l == G))) &&
+    (((o == A || o == G) && (p == C || p == U)) || ((o == C || o == U) && (p == A || p == G))))
+        return 1;
+    // or any combination of 2 unstable mismatches except AC: AA, CC, CU, GG
+    if (
+    ((k == A && l == A) || (k == C && l == C) || (k == C && l == U) || (k == U && l == C) || (k == G && l == G)) &&
+    ((o == A && p == A) || (o == C && p == C) || (o == C && p == U) || (o == U && p == C) || (o == G && p == G)))
+        return 1;
+
+    // two stabilizing mismatches (GU, GA, UU) of different sizes  (purine-purine, purine-pyrimidine, and pyrimidine-pyrimidine are different sizes)
+    if (
+    (((k == G && l == U) || (k == U && l == G)) && ((o == G && p == A) || (o == A && p == G) || (o == U && p == U))) ||
+    (((k == G && l == A) || (k == A && l == G)) && ((o == G && p == U) || (o == U && p == G) || (o == U && p == U))) ||
+    ((k == U && l == U) && ((o == G && p == A) || (o == A && p == G) || (o == G && p == U) || (o == U && p == G))))
+        return 2;
+
+    // one stable (GU, GA, UU) and one unstable mismatch (excluding AC) (AA, CC, CU, GG) of different sizes
+    // GU
+    if (((k == G && l == U) || (k == U && l == G)) && ((o == A && p == A) || (o == C && p == C) || (o == C && p == U) || (o == U && p == C) || (o == G && p == G)))
+        return 3;
+    if (((o == G && p == U) || (o == U && p == G)) && ((k == A && l == A) || (k == C && l == C) || (k == C && l == U) || (k == U && l == C) || (k == G && l == G)))
+        return 3;
+    // GA
+    if (((k == G && l == A) || (k == A && l == G)) && ((o == C && p == C) || (o == C && p == U) || (o == U && p == C)))
+        return 3;
+    if (((o == G && p == A) || (o == A && p == G)) && ((k == C && l == C) || (k == C && l == U) || (k == U && l == C)))
+        return 3;
+    // UU
+    if ((k == U && l == U) && ((o == A && p == A) || (o == G && p == G))) return 3;
+    if ((o == U && p == U) && ((k == A && l == A) || (k == G && l == G))) return 3;
+
+    return -1;
+}
+
+bool Nupack::load_parameters(const char* file)
+{
+    int p[] = {PAIR_AU, PAIR_CG, PAIR_GC, PAIR_UA, PAIR_GU, PAIR_UG};
+    int b[] = {BASE_A - 1, BASE_C - 1, BASE_G - 1, BASE_U - 1};
+
+    std::ifstream is(file);
+    if (!is) return false;
+
+    string line;
+
+    // stack
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 6; ++i) {
+        std::istringstream ss(line);
+        for (int j = 0; j != 6; ++j) {
+            int v;
+            ss >> v;
+            stack37[p[i]][p[j]] = v / 100.0;
+        }
+        std::getline(is, line);
+    }
+
+    // hairpin
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                i, j, v;
+        std::istringstream ss(line);
+        for (i = 0; i < 30 && ss; ++i) {
+            ss >> v;
+            hairpin37[i] = v / 100.0;
+        }
+        for (j = i; j < 30; ++j) hairpin37[j] = hairpin37[i - 1] + loop_greater30 * LOG((j + 1) / (1.0 * i));
+    }
+
+    // bulge
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                i, j, v;
+        std::istringstream ss(line);
+        for (i = 0; i < 30 && ss; ++i) {
+            ss >> v;
+            bulge37[i] = v / 100.0;
+        }
+        for (j = i; j < 30; ++j) bulge37[j] = bulge37[i - 1] + loop_greater30 * LOG((j + 1) / (1.0 * i));
+    }
+
+
+    // interior
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                i, j, v;
+        std::istringstream ss(line);
+        for (i = 0; i < 30 && ss; ++i) {
+            ss >> v;
+            interior37[i] = v / 100.0;
+        }
+        for (j = i; j < 30; ++j) interior37[j] = interior37[i - 1] + loop_greater30 * LOG((j + 1) / (1.0 * i));
+    }
+
+    // asymmetry panelties
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                v;
+        std::istringstream ss(line);
+        for (int i = 0; i < 4; ++i) {
+            ss >> v;
+            asymmetry_penalty[i] = v / 100.0;
+        }
+        ss >> v;
+        max_asymmetry = v / 100.0;
+    }
+
+    // triloops
+    // std::fill(triloop37.data(), triloop37.data()+triloop37.num_elements(), 0.0);
+    std::fill(&triloop37[0][0][0][0][0], &triloop37[0][0][0][0][0] + 4 * 4 * 4 * 4 * 4, 0.0);
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    while (line[0] != '>') {
+        int  v;
+        char loop[256];
+        sscanf(line.c_str(), "%s %d", loop, &v);
+        vector<int> idx(5);
+        for (int i = 0; i != 5; ++i) idx[i] = base(loop[i]) - 1;
+        // triloop37(idx) = v/100.0;
+        triloop37[idx[0]][idx[1]][idx[2]][idx[3]][idx[4]] = v / 100.0;
+        std::getline(is, line);
+    }
+
+    // tloops
+    // std::fill(tloop37.data(), tloop37.data()+tloop37.num_elements(), 0.0);
+    std::fill(&tloop37[0][0][0][0][0][0], &tloop37[0][0][0][0][0][0] + 4 * 4 * 4 * 4 * 4 * 4, 0.0);
+    std::getline(is, line);
+    while (line[0] == '>') std::getline(is, line);
+    while (line[0] != '>') {
+        int  v;
+        char loop[256];
+        sscanf(line.c_str(), "%s %d", loop, &v);
+        vector<int> idx(6);
+        for (int i = 0; i != 6; ++i) idx[i] = base(loop[i]) - 1;
+        // tloop37(idx) = v/100.0;
+        tloop37[idx[0]][idx[1]][idx[2]][idx[3]][idx[4]][idx[5]] = v / 100.0;
+        std::getline(is, line);
+    }
+
+    // mismatch hairpin
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 4; ++i) {
+        for (int j = 0; j != 4; ++j) {
+            std::istringstream ss(line);
+            for (int k = 0; k != 6; ++k) {
+                int v;
+                ss >> v;
+                mismatch_hairpin37[b[i]][b[j]][p[k]] = v / 100.0;
+            }
+            std::getline(is, line);
+        }
+    }
+
+    // mismatch interior
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 4; ++i) {
+        for (int j = 0; j != 4; ++j) {
+            std::istringstream ss(line);
+            for (int k = 0; k != 6; ++k) {
+                int v;
+                ss >> v;
+                mismatch_interior37[b[i]][b[j]][p[k]] = v / 100.0;
+            }
+            std::getline(is, line);
+        }
+    }
+
+    // dangle5
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 6; ++i) {
+        std::istringstream ss(line);
+        for (int j = 0; j != 4; ++j) {
+            int v;
+            ss >> v;
+            dangle5_37[p[i]][b[j]] = v / 100.0;
+        }
+        std::getline(is, line);
+    }
+
+    // dangle3
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 6; ++i) {
+        std::istringstream ss(line);
+        for (int j = 0; j != 4; ++j) {
+            int v;
+            ss >> v;
+            dangle3_37[p[i]][b[j]] = v / 100.0;
+        }
+        std::getline(is, line);
+    }
+
+    // multiloop penalties
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                v;
+        std::istringstream ss(line);
+        ss >> v;
+        multiloop_penalty = v / 100.0;
+        ss >> v;
+        multiloop_paired_penalty = v / 100.0;
+        ss >> v;
+        multiloop_unpaired_penalty = v / 100.0;
+        std::getline(is, line);
+    }
+
+    // AT terminate penalties
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                v;
+        std::istringstream ss(line);
+        ss >> v;
+        at_penalty = v / 100.0;
+        std::getline(is, line);
+    }
+
+    // interior loops 1x1
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 6; ++i) {
+        for (int j = 0; j != 6; ++j) {
+            std::getline(is, line);    // header
+            for (int k = 0; k != 4; ++k) {
+                std::istringstream ss(line);
+                for (int l = 0; l != 4; ++l) {
+                    int v;
+                    ss >> v;
+                    int11_37[p[i]][p[j]][b[k]][b[l]] = v / 100.0;
+                }
+                std::getline(is, line);
+            }
+        }
+    }
+
+    // interior loops 2x2
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 6; ++i) {
+        for (int j = 0; j != 6; ++j) {
+            for (int m = 0; m != 4; ++m) {
+                for (int n = 0; n != 4; ++n) {
+                    std::getline(is, line);    // header
+                    for (int k = 0; k != 4; ++k) {
+                        std::istringstream ss(line);
+                        for (int l = 0; l != 4; ++l) {
+                            int v;
+                            ss >> v;
+                            int22_37[p[i]][p[j]][b[m]][b[l]][b[n]][b[k]] = v / 100.0;
+                        }
+                        std::getline(is, line);
+                    }
+                }
+            }
+        }
+    }
+
+    // interior loops 1x2
+    while (line[0] == '>') std::getline(is, line);
+    for (int i = 0; i != 6; ++i) {
+        for (int j = 0; j != 6; ++j) {
+            for (int m = 0; m != 4; ++m) {
+                std::getline(is, line);    // header
+                for (int k = 0; k != 4; ++k) {
+                    std::istringstream ss(line);
+                    for (int l = 0; l != 4; ++l) {
+                        int v;
+                        ss >> v;
+                        int21_37[p[i]][b[k]][b[m]][p[j]][b[l]] = v / 100.0;
+                    }
+                    std::getline(is, line);
+                }
+            }
+        }
+    }
+
+    // polyC hairpin parameters
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                v;
+        std::istringstream ss(line);
+        ss >> v;
+        polyC_penalty = v / 100.0;
+        ss >> v;
+        polyC_slope = v / 100.0;
+        ss >> v;
+        polyC_int = v / 100.0;
+        std::getline(is, line);
+    }
+
+    // pseudoknot energy parameters
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                v;
+        std::istringstream ss(line);
+        ss >> v;
+        pk_penalty = v / 100.0;
+        ss >> v;
+        pk_paired_penalty = v / 100.0;
+        ss >> v;
+        pk_unpaired_penalty = v / 100.0;
+        ss >> v;
+        pk_multiloop_penalty = v / 100.0;
+        ss >> v;
+        pk_pk_penalty = v / 100.0;
+        std::getline(is, line);
+    }
+    pk_band_penalty               = 0.0;
+    pk_stack_span                 = 1.0;
+    pk_interior_span              = 1.0;
+    multiloop_penalty_pk          = multiloop_penalty;
+    multiloop_paired_penalty_pk   = multiloop_paired_penalty;
+    multiloop_unpaired_penalty_pk = multiloop_unpaired_penalty;
+
+    // BIMOLECULAR TERM
+    while (line[0] == '>') std::getline(is, line);
+    {
+        int                v;
+        std::istringstream ss(line);
+        ss >> v;
+        intermolecular_initiation = v / 100.0;
+        std::getline(is, line);
+    }
+
+    return true;
+}
+
+void Nupack::load_default_parameters()
+{
+    int p[] = {PAIR_AU, PAIR_CG, PAIR_GC, PAIR_UA, PAIR_GU, PAIR_UG};
+    int b[] = {BASE_A - 1, BASE_C - 1, BASE_G - 1, BASE_U - 1};
+
+    const int* v = &thermo_params[0];
+
+    // stack
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j) stack37[p[i]][p[j]] = *(v++) / 100.0;
+
+    // hairpin
+    for (int i = 0; i < 30; ++i) hairpin37[i] = *(v++) / 100.0;
+
+    // bulge
+    for (int i = 0; i < 30; ++i) bulge37[i] = *(v++) / 100.0;
+
+    // interior
+    for (int i = 0; i < 30; ++i) interior37[i] = *(v++) / 100.0;
+
+    // asymmetry panelties
+    for (int i = 0; i < 4; ++i) asymmetry_penalty[i] = *(v++) / 100.0;
+
+    // mismatch hairpin
+    for (int i = 0; i != 4; ++i)
+        for (int j = 0; j != 4; ++j)
+            for (int k = 0; k != 6; ++k) mismatch_hairpin37[b[i]][b[j]][p[k]] = *(v++) / 100.0;
+
+    // mismatch interior
+    for (int i = 0; i != 4; ++i)
+        for (int j = 0; j != 4; ++j)
+            for (int k = 0; k != 6; ++k) mismatch_interior37[b[i]][b[j]][p[k]] = *(v++) / 100.0;
+
+    // dangle5
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 4; ++j) dangle5_37[p[i]][b[j]] = *(v++) / 100.0;
+
+    // dangle3
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 4; ++j) dangle3_37[p[i]][b[j]] = *(v++) / 100.0;
+
+    // multiloop penalties
+    multiloop_penalty          = *(v++) / 100.0;
+    multiloop_paired_penalty   = *(v++) / 100.0;
+    multiloop_unpaired_penalty = *(v++) / 100.0;
+
+    // AT terminate penalties
+    at_penalty = *(v++) / 100.0;
+
+    // interior loops 1x1
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j)
+            for (int k = 0; k != 4; ++k)
+                for (int l = 0; l != 4; ++l) int11_37[p[i]][p[j]][b[k]][b[l]] = *(v++) / 100.0;
+
+    // interior loops 2x2
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j)
+            for (int m = 0; m != 4; ++m)
+                for (int n = 0; n != 4; ++n)
+                    for (int k = 0; k != 4; ++k)
+                        for (int l = 0; l != 4; ++l) int22_37[p[i]][p[j]][b[m]][b[l]][b[n]][b[k]] = *(v++) / 100.0;
+
+    // interior loops 1x2
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j)
+            for (int m = 0; m != 4; ++m)
+                for (int k = 0; k != 4; ++k)
+                    for (int l = 0; l != 4; ++l) int21_37[p[i]][b[k]][b[m]][p[j]][b[l]] = *(v++) / 100.0;
+
+    // polyC hairpin parameters
+    polyC_penalty = *(v++) / 100.0;
+    polyC_slope   = *(v++) / 100.0;
+    polyC_int     = *(v++) / 100.0;
+
+    // pseudoknot energy parameters
+    pk_penalty                    = *(v++) / 100.0;
+    pk_paired_penalty             = *(v++) / 100.0;
+    pk_unpaired_penalty           = *(v++) / 100.0;
+    pk_multiloop_penalty          = *(v++) / 100.0;
+    pk_pk_penalty                 = *(v++) / 100.0;
+    pk_band_penalty               = 0.0;
+    pk_stack_span                 = 1.0;
+    pk_interior_span              = 1.0;
+    multiloop_penalty_pk          = multiloop_penalty;
+    multiloop_paired_penalty_pk   = multiloop_paired_penalty;
+    multiloop_unpaired_penalty_pk = multiloop_unpaired_penalty;
+
+    // BIMOLECULAR TERM
+    intermolecular_initiation = *(v++) / 100.0;
+
+    // triloops
+    // std::fill(triloop37.data(), triloop37.data()+triloop37.num_elements(), 0.0);
+    std::fill(&triloop37[0][0][0][0][0], &triloop37[0][0][0][0][0] + 4 * 4 * 4 * 4 * 4, 0.0);
+    for (int i = 0; triloops[i].s != NULL; ++i) {
+        int         v    = triloops[i].e;
+        const char* loop = triloops[i].s;
+        vector<int> idx(5);
+        for (int i = 0; i != 5; ++i) idx[i] = base(loop[i]) - 1;
+        // triloop37(idx) = v/100.0;
+        triloop37[idx[0]][idx[1]][idx[2]][idx[3]][idx[4]] = v / 100.0;
+    }
+
+    // tloops
+    // std::fill(tloop37.data(), tloop37.data()+tloop37.num_elements(), 0.0);
+    std::fill(&tloop37[0][0][0][0][0][0], &tloop37[0][0][0][0][0][0] + 4 * 4 * 4 * 4 * 4 * 4, 0.0);
+    for (int i = 0; tetraloops[i].s != NULL; ++i) {
+        int         v    = tetraloops[i].e;
+        const char* loop = tetraloops[i].s;
+        vector<int> idx(6);
+        for (int i = 0; i != 6; ++i) idx[i] = base(loop[i]) - 1;
+        // tloop37(idx) = v/100.0;
+        tloop37[idx[0]][idx[1]][idx[2]][idx[3]][idx[4]][idx[5]] = v / 100.0;
+    }
+}
+
+void Nupack::dump_parameters(std::ostream& os) const
+{
+    // stack
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j) os << "stack37[" << i << "][" << j << "]=" << stack37[i][j] << std::endl;
+
+    // hairpin
+    for (int i = 0; i != 30; ++i) os << "hairpin37[" << i << "]=" << hairpin37[i] << std::endl;
+
+    // bulge
+    for (int i = 0; i != 30; ++i) os << "bulge37[" << i << "]=" << bulge37[i] << std::endl;
+
+    // interior
+    for (int i = 0; i != 30; ++i) os << "interior37[" << i << "]=" << interior37[i] << std::endl;
+
+    // asymmetry
+    for (int i = 0; i != 4; ++i) os << "asymmetry_penalty[" << i << "]=" << asymmetry_penalty[i] << std::endl;
+    os << "max_asymmetry=" << max_asymmetry << std::endl;
+
+    // triloops
+    for (int i0 = 0; i0 != 4; ++i0)
+        for (int i1 = 0; i1 != 4; ++i1)
+            for (int i2 = 0; i2 != 4; ++i2)
+                for (int i3 = 0; i3 != 4; ++i3)
+                    for (int i4 = 0; i4 != 4; ++i4)
+                        if (triloop37[i0][i1][i2][i3][i4] != 0.0)
+                            os << "triloop37[" << i0 << "][" << i1 << "][" << i2 << "][" << i3 << "][" << i4
+                               << "]=" << triloop37[i0][i1][i2][i3][i4] << std::endl;
+
+    // tloops
+    for (int i0 = 0; i0 != 4; ++i0)
+        for (int i1 = 0; i1 != 4; ++i1)
+            for (int i2 = 0; i2 != 4; ++i2)
+                for (int i3 = 0; i3 != 4; ++i3)
+                    for (int i4 = 0; i4 != 4; ++i4)
+                        for (int i5 = 0; i5 != 4; ++i5)
+                            if (tloop37[i0][i1][i2][i3][i4][i5] != 0.0)
+                                os << "tloop37[" << i0 << "][" << i1 << "][" << i2 << "][" << i3 << "][" << i4 << "]["
+                                   << i5 << "]=" << tloop37[i0][i1][i2][i3][i4][i5] << std::endl;
+
+    // mismatch hairpin
+    for (int i = 0; i != 4; ++i)
+        for (int j = 0; j != 4; ++j)
+            for (int k = 0; k != 6; ++k)
+                os << "mismatch_hairpin37[" << i << "][" << j << "][" << k << "]=" << mismatch_hairpin37[i][j][k] << std::endl;
+
+    // mismatch interior37
+    for (int i = 0; i != 4; ++i)
+        for (int j = 0; j != 4; ++j)
+            for (int k = 0; k != 6; ++k)
+                os << "mismatch_interior37[" << i << "][" << j << "][" << k << "]=" << mismatch_interior37[i][j][k] << std::endl;
+
+    // dangle5
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 4; ++j) os << "dangle5_37[" << i << "][" << j << "]=" << dangle5_37[i][j] << std::endl;
+
+    // dangle3
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 4; ++j) os << "dangle3_37[" << i << "][" << j << "]=" << dangle3_37[i][j] << std::endl;
+
+    // multiloop penalties
+    os << "multiloop_penalty=" << multiloop_penalty << std::endl
+       << "multiloop_paired_penalty=" << multiloop_paired_penalty << std::endl
+       << "multiloop_unpaired_penalty=" << multiloop_unpaired_penalty << std::endl;
+
+    // AT terminate penalties
+    os << "at_penalty=" << at_penalty << std::endl;
+
+    // interior loops 1x1
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j)
+            for (int k = 0; k != 4; ++k)
+                for (int l = 0; l != 4; ++l)
+                    os << "int11_37[" << i << "][" << j << "][" << k << "][" << l << "]=" << int11_37[i][j][k][l] << std::endl;
+
+    // interior loops 2x2
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j)
+            for (int m = 0; m != 4; ++m)
+                for (int n = 0; n != 4; ++n)
+                    for (int k = 0; k != 4; ++k)
+                        for (int l = 0; l != 4; ++l)
+                            os << "int22_37[" << i << "][" << j << "][" << m << "][" << l << "][" << n << "][" << k
+                               << "]=" << int22_37[i][j][m][l][n][k] << std::endl;
+
+    // interior loops 1x2
+    for (int i = 0; i != 6; ++i)
+        for (int j = 0; j != 6; ++j)
+            for (int m = 0; m != 4; ++m)
+                for (int k = 0; k != 4; ++k)
+                    for (int l = 0; l != 4; ++l)
+                        os << "int21_37[" << i << "][" << k << "][" << m << "][" << j << "][" << l
+                           << "]=" << int21_37[i][k][m][j][l] << std::endl;
+
+    // polyC hairpin parameters
+    os << "polyC_penalty=" << polyC_penalty << std::endl
+       << "polyC_slope=" << polyC_slope << std::endl
+       << "polyC_int=" << polyC_int << std::endl;
+
+    // pseudoknot energy parameters
+    os << "pk_penalty=" << pk_penalty << std::endl
+       << "pk_paired_penalty=" << pk_paired_penalty << std::endl
+       << "pk_unpaired_penalty=" << pk_unpaired_penalty << std::endl
+       << "pk_multiloop_penalty=" << pk_multiloop_penalty << std::endl
+       << "pk_pk_penalty=" << pk_pk_penalty << std::endl
+       << "pk_band_penalty=" << pk_band_penalty << std::endl
+       << "pk_stack_span=" << pk_stack_span << std::endl
+       << "pk_interior_span=" << pk_interior_span << std::endl
+       << "multiloop_penalty_pk=" << multiloop_penalty_pk << std::endl
+       << "multiloop_paired_penalty_pk=" << multiloop_paired_penalty_pk << std::endl
+       << "multiloop_unpaired_penalty_pk" << multiloop_unpaired_penalty_pk << std::endl;
+
+    // BIMOLECULAR TERM
+    os << "intermolecular_initiation=" << intermolecular_initiation << std::endl;
+
+    // misc
+    os << "loop_greater30=" << loop_greater30 << std::endl << "hairpin_GGG=" << hairpin_GGG << std::endl;
+}
+
+float Nupack::calculate_partition_function()
+{
+    Q.resize(N);
+    Q.fill(0.0);
+    Qb.resize(N);
+    Qb.fill(0.0);
+    Qm.resize(N);
+    Qm.fill(0.0);
+    Qp.resize(N);
+    Qp.fill(0.0);
+    Qz.resize(N);
+    Qz.fill(0.0);
+    std::cout << "ça passe 5!" << std::endl;
+    Qg.resize(N);
+    std::cout << "ah tiens." << std::endl;
+    Qg.fill(0.0);
+    std::cout << "ça passe 6!" << std::endl;
+    Qgl.resize(N);
+    Qgl.fill(0.0);
+    Qgr.resize(N);
+    Qgr.fill(0.0);
+    Qgls.resize(N);
+    Qgls.fill(0.0);
+    Qgrs.resize(N);
+    Qgrs.fill(0.0);
+    for (int i = 0; i != N; ++i) Q(i, i - 1) = Qz(i, i - 1) = 1.0;
+    DPtableX Qx, Qx1, Qx2;
+
+    for (int l = 1; l <= N; ++l) {
+        Qx.swap(Qx1);
+        Qx1.swap(Qx2);
+        Qx2.resize(l + 1, N);
+        Qx2.fill(0.0);
+
+        for (int i = 0; i + l <= N; ++i) {
+            int j = i + l - 1;
+
+            // Qb recursion
+            if (allow_paired(i, j)) {
+                Qb(i, j) = EXP(-score_hairpin(i, j) / RT);
+
+                for (int d = i + 1; d <= j - 5; ++d)    // all possible rightmost pairs d-e
+                {
+                    for (int e = d + 4; e <= j - 1; ++e) {
+                        if (allow_paired(d, e)) {
+                            Qb(i, j) += Qb(d, e) * EXP(-score_interior(i, d, e, j, false) / RT);
+
+                            if (d >= i + 6 && wc_pair(d, e) && wc_pair(i, j)) {
+                                Qb(i, j) += Qm(i + 1, d - 1) * Qb(d, e) *
+                                            EXP(
+                                            -(
+                                            score_multiloop(false) + score_multiloop_paired(2, false) +
+                                            score_multiloop_unpaired(j - e - 1, false) + score_at_penalty(i, j) +
+                                            score_at_penalty(d, e) + score_dangle(e + 1, j - 1)) /
+                                            RT);
+                            }
+                        }
+                    }
+                }
+
+                if (wc_pair(i, j)) {
+                    for (int d = i + 1; d <= j - 6; ++d)    // all possible rightmost pseudoknots filling [d,e]
+                    {
+                        for (int e = d + 5; e <= j - 1; ++e) {
+                            Qb(i, j) +=
+                            Qp(d, e) * EXP(
+                                       -(
+                                       score_multiloop(false) + score_pk_multiloop() + score_multiloop_paired(3, false) +
+                                       score_multiloop_unpaired(j - e - 1 + d - i - 1, false) + score_at_penalty(i, j) +
+                                       score_dangle(e + 1, j - 1) + score_dangle(i + 1, d - 1)) /
+                                       RT);
+
+                            Qb(i, j) +=
+                            Qm(i + 1, d - 1) * Qp(d, e) *
+                            EXP(
+                            -(
+                            score_multiloop(false) + score_pk_multiloop() + score_multiloop_paired(3, false) +
+                            score_multiloop_unpaired(j - e - 1, false) + score_at_penalty(i, j) + score_dangle(e + 1, j - 1)) /
+                            RT);
+                        }
+                    }
+                }
+            }
+
+            // Qg recursion
+            if (allow_paired(i, j)) {
+                // case 0: only 1 pair
+                Qg(i, i, j, j) = 1;
+
+                // case 1: terminal inner pair
+                for (int d = i + 1; d <= j - 5; ++d) {
+                    for (int e = d + 4; e <= j - 1; ++e) {
+                        if (allow_paired(d, e)) Qg(i, d, e, j) += EXP(-score_interior(i, d, e, j, true) / RT);
+                    }
+                }
+            }
+
+            fastiloops(i, j, Qg, Qx, Qx2);
+
+            if (allow_paired(i, j) && wc_pair(i, j)) {
+
+                // case 2: multiloop left
+                for (int d = i + 6; d <= j - 5; ++d) {
+                    for (int e = d + 4; e <= j - 1; ++e) {
+                        if (allow_paired(d, e) && wc_pair(d, e)) {
+                            Qg(i, d, e, j) +=
+                            Qm(i + 1, d - 1) *
+                            EXP(
+                            -(
+                            score_multiloop(true) + score_multiloop_paired(2, true) + score_multiloop_unpaired(j - e - 1, true) +
+                            score_at_penalty(i, j) + score_at_penalty(d, e) + score_dangle(e + 1, j - 1)) /
+                            RT);
+                        }
+                    }
+                }
+
+                // case 3: multiloop right
+                for (int d = i + 1; d <= j - 10; ++d) {
+                    for (int e = d + 4; e <= j - 6; ++e) {
+                        if (allow_paired(d, e) && wc_pair(d, e)) {
+                            Qg(i, d, e, j) +=
+                            Qm(e + 1, j - 1) *
+                            EXP(
+                            -(
+                            score_multiloop(true) + score_multiloop_paired(2, true) + score_multiloop_unpaired(d - i - 1, true) +
+                            score_at_penalty(i, j) + score_at_penalty(d, e) + score_dangle(i + 1, d - 1)) /
+                            RT);
+                        }
+                    }
+                }
+
+                // case 4: multiloop both sides
+                for (int d = i + 6; d <= j - 10; ++d) {
+                    for (int e = d + 4; e <= j - 6; ++e) {
+                        if (allow_paired(d, e) && wc_pair(d, e)) {
+                            Qg(i, d, e, j) +=
+                            Qm(i + 1, d - 1) * Qm(e + 1, j - 1) *
+                            EXP(-(score_multiloop(true) + score_multiloop_paired(2, true) + score_at_penalty(i, j) + score_at_penalty(d, e)) / RT);
+                        }
+                    }
+                }
+
+                // case 5: interior loop + multi left
+                for (int d = i + 7; d <= j - 6; ++d) {
+                    for (int e = d + 4; e <= j - 2; ++e) {
+                        if (allow_paired(d, e)) {
+                            for (int f = e + 1; f <= j - 1; ++f) {
+                                Qg(i, d, e, j) +=
+                                Qgls(i + 1, d, e, f) * EXP(
+                                                       -(
+                                                       score_multiloop(true) + score_multiloop_paired(1, true) +
+                                                       score_multiloop_unpaired(j - f - 1, true) +
+                                                       score_at_penalty(i, j) + score_dangle(f + 1, j - 1)) /
+                                                       RT);
+                            }
+                        }
+                    }
+                }
+
+                // case 6: interior loop + multi right
+                for (int d = i + 2; d <= j - 11; ++d) {
+                    for (int e = d + 4; e <= j - 7; ++e) {
+                        if (allow_paired(d, e)) {
+                            for (int c = i + 1; c <= d - 1; ++c) {
+                                Qg(i, d, e, j) +=
+                                Qgrs(c, d, e, j - 1) * EXP(
+                                                       -(
+                                                       score_multiloop(true) + score_multiloop_paired(1, true) +
+                                                       score_multiloop_unpaired(c - i - 1, true) +
+                                                       score_at_penalty(i, j) + score_dangle(i + 1, c - 1)) /
+                                                       RT);
+                            }
+                        }
+                    }
+                }
+
+                // case 7: interior loop + multi both sides
+                for (int d = i + 7; d <= j - 11; ++d) {
+                    for (int e = d + 4; e <= j - 7; ++e) {
+                        if (allow_paired(d, e)) {
+                            for (int c = i + 6; c <= d - 1; ++c) {
+                                Qg(i, d, e, j) +=
+                                Qm(i + 1, c - 1) * Qgrs(c, d, e, j - 1) *
+                                EXP(-(score_multiloop(true) + score_multiloop_paired(1, true) + score_at_penalty(i, j)) / RT);
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Qgls recursion
+            for (int c = i + 5; c <= j - 6; ++c) {
+                if (allow_paired(c, j) && wc_pair(c, j)) {
+                    for (int d = c + 1; d <= j - 5; ++d) {
+                        for (int e = d + 4; e <= j - 1; ++e) {
+                            if (allow_paired(d, e)) {
+                                Qgls(i, d, e, j) += Qm(i, c - 1) * Qg(c, d, e, j) *
+                                                    EXP(-(score_multiloop_paired(1, true) + score_at_penalty(c, j)) / RT);
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Qgrs recursion
+            for (int d = i + 1; d <= j - 10; ++d) {
+                for (int e = d + 4; e <= j - 6; ++e) {
+                    if (allow_paired(d, e)) {
+                        for (int f = e + 1; f <= j - 5; ++f) {
+                            if (allow_paired(i, f) && wc_pair(i, f)) {
+                                Qgrs(i, d, e, j) += Qg(i, d, e, f) * Qm(f + 1, j) *
+                                                    EXP(-(score_multiloop_paired(1, true) + score_at_penalty(i, f)) / RT);
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Qgl recursions
+            for (int d = i + 1; d <= j - 5; ++d) {
+                for (int f = d + 4; f <= j - 1; ++f) {
+                    if (allow_paired(d, f) && wc_pair(d, f)) {
+                        for (int e = d; e <= f - 2; ++e)    // f-3???
+                        {
+                            Qgl(i, e, f, j) +=
+                            Qg(i, d, f, j) * Qz(d + 1, e) * EXP(-(score_pk_paired(1) + score_at_penalty(d, f)) / RT);
+                        }
+                    }
+                }
+            }
+
+            // Qgr recursion
+            for (int d = i + 1; d <= j - 3; ++d) {
+                for (int e = d + 2; e <= j - 1; ++e) {
+                    for (int f = e; f <= j - 1; ++f) {
+                        Qgr(i, d, e, j) += Qgl(i, d, f, j) * Qz(e, f - 1);
+                    }
+                }
+            }
+
+            // Qp recursion
+            // case 1: both Qg are exactly 1 pair
+            // first case is exactly 1 pair per Og
+            if (j - i > 4) {
+                int a = i;
+                int f = j;
+                for (int b = a + 1; b <= j - 4; ++b) {
+                    if (allow_paired(b, j) && wc_pair(b, j)) {
+                        int c = b;
+                        for (int d = std::max(c + 1, a + 4); d <= j - 1; ++d) {
+                            if (allow_paired(a, d) && wc_pair(a, d)) {
+                                int e = d;
+                                Qp(i, j) += Qg(i, a, d, e) * Qg(b, c, f, j) * Qz(e + 1, f - 1) * Qz(c + 1, d - 1) *
+                                            Qz(a + 1, b - 1) *
+                                            EXP(
+                                            -(
+                                            score_pk_paired(2) + score_pk_band(2) + score_at_penalty(a, d) +
+                                            score_at_penalty(c, f) + score_at_penalty(i, e) + score_at_penalty(b, j)) /
+                                            RT);
+                            }
+                        }
+                    }
+                }
+            }
+
+            if (j - i > 6) {
+                // case 2 left Og is exactly 1 pair, right is 2+
+                for (int d = i + 1; d <= j - 6; ++d) {
+                    if (allow_paired(d, j) && wc_pair(d, j)) {
+                        for (int e = std::max(d + 2, i + 4); e <= j - 2; ++e) {
+                            int f = e;
+                            if (allow_paired(i, f) && wc_pair(i, f)) {
+                                Qp(i, j) +=
+                                Qg(i, i, e, f) * Qz(i + 1, d - 1) * Qgr(d, e - 1, f + 1, j) *
+                                EXP(-(score_pk_paired(1) + score_pk_band(2) + score_at_penalty(d, j) + score_at_penalty(i, f) * 2) / RT);
+                            }
+                        }
+                    }
+                }
+
+                // case 2 left Qg is 2+ pairs, right is 1
+                for (int d = i + 2; d <= j - 4; ++d) {
+                    if (allow_paired(d, j) && wc_pair(d, j)) {
+                        for (int e = std::max(d + 1, i + 4); e <= j - 2; ++e) {
+                            for (int f = e + 1; f <= j - 1; ++f) {
+                                if (allow_paired(i, f) && wc_pair(i, f)) {
+                                    Qp(i, j) +=
+                                    Qgl(i, d - 1, e, f) * Qg(d, d, j, j) * Qz(d + 1, e - 1) * Qz(f + 1, j - 1) *
+                                    EXP(-(score_pk_paired(1) + score_pk_band(2) + score_at_penalty(d, j) * 2 + score_at_penalty(i, f)) / RT);
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+
+            // otherwise
+            if (j - i > 7) {
+                for (int d = i + 2; d <= j - 4; ++d) {
+                    if (allow_paired(d, j) && wc_pair(d, j)) {
+                        for (int e = std::max(d + 2, i + 5); e <= j - 3; ++e) {
+                            for (int f = e + 1; f <= j - 2; ++f) {
+                                if (allow_paired(i, f) && wc_pair(i, f)) {
+                                    Qp(i, j) += Qgl(i, d - 1, e, f) * Qgr(d, e - 1, f + 1, j) *
+                                                EXP(-(score_pk_band(2) + score_at_penalty(d, j) + score_at_penalty(i, j)) / RT);
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Q, Qm, Qz recursions
+            Q(i, j) = EXP(-score_dangle(i, j) / RT);    // empty recursion
+
+            if (i != 0 && j != N - 1) {
+                Qz(i, j) = EXP(-(score_dangle(i, j) + score_pk_unpaired(j - i + 1)) / RT);
+            }
+
+            for (int d = i; d <= j - 4; ++d) {
+                for (int e = d + 4; e <= j; ++e) {
+                    if (allow_paired(d, e) && wc_pair(d, e)) {
+                        Q(i, j) += Q(i, d - 1) * Qb(d, e) * EXP(-(score_at_penalty(d, e) + score_dangle(e + 1, j)) / RT);
+
+                        if (i != 0 && j != N - 1) {
+                            Qm(i, j) +=
+                            Qb(d, e) * EXP(
+                                       -(
+                                       score_multiloop_paired(1, false) + score_multiloop_unpaired(d - i + j - e, false) +
+                                       score_at_penalty(d, e) + score_dangle(e + 1, j) + score_dangle(i, d - 1)) /
+                                       RT);
+
+                            if (d >= i + 5) {
+                                Qm(i, j) += Qm(i, d - 1) * Qb(d, e) *
+                                            EXP(
+                                            -(
+                                            score_multiloop_paired(1, false) + score_multiloop_unpaired(j - e, false) +
+                                            score_at_penalty(d, e) + score_dangle(e + 1, j)) /
+                                            RT);
+                            }
+
+                            Qz(i, j) +=
+                            Qz(i, d - 1) * Qb(d, e) *
+                            EXP(-(score_pk_paired(1) + score_pk_unpaired(j - e) + score_at_penalty(d, e) + score_dangle(e + 1, j)) / RT);
+                        }
+                    }
+                }
+            }
+
+            for (int d = i; d <= j - 5; ++d) {
+                for (int e = d + 5; e <= j; ++e) {
+                    Q(i, j) += Q(i, d - 1) * Qp(d, e) * EXP(-(score_pk() + score_dangle(e + 1, j)) / RT);
+
+                    if (i != 0 && j != N - 1) {
+                        Qm(i, j) += Qp(d, e) * EXP(
+                                               -(
+                                               score_pk_multiloop() + score_multiloop_paired(2, false) +
+                                               score_multiloop_unpaired(d - i + j - e, false) + score_dangle(e + 1, j) +
+                                               score_dangle(i, d - 1)) /
+                                               RT);
+
+                        if (d >= i + 5) {
+                            Qm(i, j) += Qm(i, d - 1) * Qp(d, e) *
+                                        EXP(
+                                        -(
+                                        score_pk_multiloop() + score_multiloop_paired(2, false) +
+                                        score_multiloop_unpaired(j - e, false) + score_dangle(e + 1, j)) /
+                                        RT);
+                        }
+
+                        Qz(i, j) +=
+                        Qz(i, d - 1) * Qp(d, e) *
+                        EXP(-(score_pk_pk() + score_pk_paired(2) + score_pk_unpaired(j - e) + score_dangle(e + 1, j)) / RT);
+                    }
+                }
+            }
+            // printf("%d,%d: %Lf\n", i, j, Q(i,j));
+        }
+    }
+
+    return Q(0, N - 1);
+}
+
+void Nupack::fastiloops(int i, int j, DPtable4& Qg, DPtableX& Qx, DPtableX& Qx2)
+{
+    int l = j - i + 1;
+    if (l >= 17)    // smallest subsequence not added to Qg as special case
+    {
+        for (int d = i + 6; d <= j - 10; ++d) {
+            for (int e = d + 4; e <= j - 6; ++e) {
+                if (allow_paired(d, e)) {
+                    int l1 = 4;    // explicitly add in terms for l1=4, l2>=4
+                    int c  = i + l1 + 1;
+                    for (int l2 = 4; l2 <= j - e - 2; ++l2) {
+                        int s = l1 + l2;
+                        int f = j - l2 - 1;
+                        if (allow_paired(c, f)) {
+                            Qx(i, d, e, s) +=
+                            Qg(c, d, e, f) *
+                            EXP(-(score_interior_asymmetry(l1, l2) + score_interior_mismatch(f, c, f + 1, c - 1)) / RT);
+                        }
+                    }
+
+                    if (d >= i + 7) {
+                        int l2 = 4;    // explicitly add in terms of l1>=5, l2=4
+                        int f  = j - l2 - 1;
+                        for (int l1 = 5; l1 <= d - i - 2; ++l1) {
+                            int s = l1 + l2;
+                            int c = i + l1 + 1;
+                            if (allow_paired(c, f)) {
+                                Qx(i, d, e, s) +=
+                                Qg(c, d, e, f) *
+                                EXP(-(score_interior_asymmetry(l1, l2) + score_interior_mismatch(f, c, f + 1, c - 1)) / RT);
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    for (int d = i + 1; d <= j - 5; ++d) {
+        for (int e = d + 4; e <= j - 1; ++e) {
+            if (allow_paired(d, e)) {
+                // convert Qx into interior loop energies
+                if (l >= 17 && allow_paired(i, j)) {
+                    for (int s = 8; s <= l - 9; ++s) {
+                        Qg(i, d, e, j) += Qx(i, d, e, s) * EXP(-score_interior_mismatch(i, j, i + 1, j - 1) / RT);
+                    }
+                }
+
+                // extend loops for future use
+                if (i != 0 && j != N - 1) {
+                    for (int s = 8; s <= l - 9; ++s) {
+                        Qx2(i - 1, d, e, s + 2) = Qx(i, d, e, s) * EXP(-(score_loop(s + 2) - score_loop(s)) / RT);
+                    }
+                }
+
+                if (allow_paired(i, j)) {
+                    // Add small inextensible interior loops to Qg as special cases
+                    for (int l1 = 0; l1 <= std::min(3, d - i - 2); ++l1) {
+                        int c = i + l1 + 1;
+                        for (int l2 = 0; l2 <= std::min(3, j - e - 2); ++l2) {
+                            int f = j - l2 - 1;
+                            if (allow_paired(c, f)) {
+                                Qg(i, d, e, j) += Qg(c, d, e, f) * EXP(-score_interior(i, c, f, j, true) / RT);
+                            }
+                        }
+                    }
+                    // Add bulge loops and large asymmetric loops as special cases
+                    for (int l1 = 0; l1 <= std::min(3, d - i - 2); ++l1)    // cases l1=0,1,2,3, l2>=4
+                    {
+                        int c = i + l1 + 1;
+                        for (int l2 = 4; l2 <= j - e - 2; ++l2) {
+                            int f = j - l2 - 1;
+                            if (allow_paired(c, f)) {
+                                Qg(i, d, e, j) += Qg(c, d, e, f) * EXP(-score_interior(i, c, f, j, true) / RT);
+                            }
+                        }
+                    }
+                    for (int l2 = 0; l2 <= std::min(3, j - e - 2); ++l2) {
+                        int f = j - l2 - 1;
+                        for (int l1 = 4; l1 <= d - i - 2; ++l1) {
+                            int c = i + l1 + 1;
+                            if (allow_paired(c, f)) {
+                                Qg(i, d, e, j) += Qg(c, d, e, f) * EXP(-score_interior(i, c, f, j, true) / RT);
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+void Nupack::calculate_posterior()
+{
+    // std::cout << "calculate_posterior_nupack\n";
+    P.resize(N);
+    P.fill(0.0);
+    Pb.resize(N);
+    Pb.fill(0.0);
+    Pm.resize(N);
+    Pm.fill(0.0);
+    Pp.resize(N);
+    Pp.fill(0.0);
+    Pz.resize(N);
+    Pz.fill(0.0);
+    Pbg.resize(N);
+    Pbg.fill(0.0);
+    Pg.resize(N);
+    Pg.fill(0.0);
+    Pgl.resize(N);
+    Pgl.fill(0.0);
+    Pgr.resize(N);
+    Pgr.fill(0.0);
+    Pgls.resize(N);
+    Pgls.fill(0.0);
+    Pgrs.resize(N);
+    Pgrs.fill(0.0);
+    P(0, N - 1) = 1.0;
+    DPtableX Qx, Qx1, Qx2;
+    Qx.resize(N, N);
+    Qx1.resize(N - 1, N);
+    Qx2.resize(N - 2, N);
+    DPtableX Px, Px1, Px2;
+    Px.resize(N, N);
+    Px1.resize(N - 1, N);
+    Px2.resize(N - 2, N);
+
+    for (int l = N; l >= 1; --l) {
+        Qx.swap(Qx1);
+        Qx1.swap(Qx2);
+        Qx2.resize(l - 3, N);
+        Qx2.fill(0.0);
+        Px.swap(Px1);
+        Px1.swap(Px2);
+        Px2.resize(l - 3, N);
+        Px2.fill(0.0);
+
+        for (int i = 0; i + l <= N; ++i) {
+            int j = i + l - 1;
+
+            // P, Pm, Pz recursions
+            for (int d = i; d <= j - 4; ++d) {
+                for (int e = d + 4; e <= j; ++e) {
+                    if (allow_paired(d, e) && wc_pair(d, e)) {
+                        if (P(i, j) > 0.0) {
+                            float p = Q(i, d - 1) * Qb(d, e) *
+                                       EXP(-(score_at_penalty(d, e) + score_dangle(e + 1, j)) / RT) / Q(i, j) * P(i, j);
+                            P(i, d - 1) += p;
+                            Pb(d, e) += p;
+                            assert(!std::isnan(p));
+                        }
+
+                        if (i != 0 && j != N - 1) {
+                            if (Pm(i, j) > 0.0) {
+                                float p = Qb(d, e) *
+                                           EXP(
+                                           -(
+                                           score_multiloop_paired(1, false) + score_multiloop_unpaired(d - i + j - e, false) +
+                                           score_at_penalty(d, e) + score_dangle(e + 1, j) + score_dangle(i, d - 1)) /
+                                           RT) /
+                                           Qm(i, j) * Pm(i, j);
+                                Pb(d, e) += p;
+
+                                if (d >= i + 5) {
+                                    p = Qm(i, d - 1) * Qb(d, e) *
+                                        EXP(
+                                        -(
+                                        score_multiloop_paired(1, false) + score_multiloop_unpaired(j - e, false) +
+                                        score_at_penalty(d, e) + score_dangle(e + 1, j)) /
+                                        RT) /
+                                        Qm(i, j) * Pm(i, j);
+                                    Pm(i, d - 1) += p;
+                                    Pb(d, e) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+
+                            if (Pz(i, j) > 0.0) {
+                                float p =
+                                Qz(i, d - 1) * Qb(d, e) *
+                                EXP(-(score_pk_paired(1) + score_pk_unpaired(j - e) + score_at_penalty(d, e) + score_dangle(e + 1, j)) / RT) /
+                                Qz(i, j) * Pz(i, j);
+                                Pz(i, d - 1) += p;
+                                Pb(d, e) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+
+            for (int d = i; d <= j - 5; ++d) {
+                for (int e = d + 5; e <= j; ++e) {
+                    if (P(i, j) > 0.0) {
+                        float p =
+                        Q(i, d - 1) * Qp(d, e) * EXP(-(score_pk() + score_dangle(e + 1, j)) / RT) / Q(i, j) * P(i, j);
+                        P(i, d - 1) += p;
+                        Pp(d, e) += p;
+                        assert(!std::isnan(p));
+                    }
+
+                    if (i != 0 && j != N - 1) {
+                        if (Pm(i, j) > 0.0) {
+                            float p =
+                            Qp(d, e) *
+                            EXP(
+                            -(
+                            score_pk_multiloop() + score_multiloop_paired(2, false) +
+                            score_multiloop_unpaired(d - i + j - e, false) + score_dangle(e + 1, j) + score_dangle(i, d - 1)) /
+                            RT) /
+                            Qm(i, j) * Pm(i, j);
+                            Pp(d, e) += p;
+                            assert(!std::isnan(p));
+
+                            if (d >= i + 5) {
+                                p = Qm(i, d - 1) * Qp(d, e) *
+                                    EXP(
+                                    -(
+                                    score_pk_multiloop() + score_multiloop_paired(2, false) +
+                                    score_multiloop_unpaired(j - e, false) + score_dangle(e + 1, j)) /
+                                    RT) /
+                                    Qm(i, j) * Pm(i, j);
+                                Pm(i, d - 1) += p;
+                                Pp(d, e) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+
+                        if (Pz(i, j) > 0.0) {
+                            float p =
+                            Qz(i, d - 1) * Qp(d, e) *
+                            EXP(-(score_pk_pk() + score_pk_paired(2) + score_pk_unpaired(j - e) + score_dangle(e + 1, j)) / RT) /
+                            Qz(i, j) * Pz(i, j);
+                            Pz(i, d - 1) += p;
+                            Pp(d, e) += p;
+                            assert(!std::isnan(p));
+                        }
+                    }
+                }
+            }
+
+            // Pp recursion
+            // case 1: both Qg are exactly 1 pair
+            // first case is exactly 1 pair per Og
+            if (j - i > 4) {
+                int a = i;
+                int f = j;
+                for (int b = a + 1; b <= j - 4; ++b) {
+                    if (allow_paired(b, j) && wc_pair(b, j)) {
+                        int c = b;
+                        for (int d = std::max(c + 1, a + 4); d <= j - 1; ++d) {
+                            if (allow_paired(a, d) && wc_pair(a, d) && Pp(i, j) > 0.0) {
+                                int    e = d;
+                                float p = Qg(i, a, d, e) * Qg(b, c, f, j) * Qz(e + 1, f - 1) * Qz(c + 1, d - 1) *
+                                           Qz(a + 1, b - 1) *
+                                           EXP(
+                                           -(
+                                           score_pk_paired(2) + score_at_penalty(a, d) + score_at_penalty(c, f) +
+                                           score_at_penalty(i, e) + score_at_penalty(b, j)) /
+                                           RT) /
+                                           Qp(i, j) * Pp(i, j);
+                                Pg(i, a, d, e) += p;
+                                Pg(b, c, f, j) += p;
+                                Pz(e + 1, f - 1) += p;
+                                Pz(c + 1, d - 1) += p;
+                                Pz(a + 1, b - 1) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+
+            if (j - i > 6) {
+                // case 2 left Og is exactly 1 pair, right is 2+
+                for (int d = i + 1; d <= j - 6; ++d) {
+                    if (allow_paired(d, j) && wc_pair(d, j)) {
+                        for (int e = std::max(d + 2, i + 4); e <= j - 2; ++e) {
+                            int f = e;
+                            if (allow_paired(i, f) && wc_pair(i, f) && Pp(i, j) > 0.0) {
+                                float p = Qg(i, i, e, f) * Qz(i + 1, d - 1) * Qgr(d, e - 1, f + 1, j) *
+                                           EXP(-(score_pk_paired(1) + score_at_penalty(d, j) + score_at_penalty(i, f) * 2) / RT) /
+                                           Qp(i, j) * Pp(i, j);
+                                Pg(i, i, e, f) += p;
+                                Pz(i + 1, d - 1) += p;
+                                Pgr(d, e - 1, f + 1, j) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+
+                // case 2 left Qg is 2+ pairs, right is 1
+                for (int d = i + 2; d <= j - 4; ++d) {
+                    if (allow_paired(d, j) && wc_pair(d, j)) {
+                        for (int e = std::max(d + 1, i + 4); e <= j - 2; ++e) {
+                            for (int f = e + 1; f <= j - 1; ++f) {
+                                if (allow_paired(i, f) && wc_pair(i, f) && Pp(i, j) > 0.0) {
+                                    float p =
+                                    Qgl(i, d - 1, e, f) * Qg(d, d, j, j) * Qz(d + 1, e - 1) * Qz(f + 1, j - 1) *
+                                    EXP(-(score_pk_paired(1) + score_at_penalty(d, j) * 2 + score_at_penalty(i, f)) / RT) /
+                                    Qp(i, j) * Pp(i, j);
+                                    Pgl(i, d - 1, e, f) += p;
+                                    Pg(d, d, j, j) += p;
+                                    Pz(d + 1, e - 1) += p;
+                                    Pz(f + 1, j - 1) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+
+            // otherwise
+            if (j - i > 7) {
+                for (int d = i + 2; d <= j - 4; ++d) {
+                    if (allow_paired(d, j) && wc_pair(d, j)) {
+                        for (int e = std::max(d + 2, i + 5); e <= j - 3; ++e) {
+                            for (int f = e + 1; f <= j - 2; ++f) {
+                                if (allow_paired(i, f) && wc_pair(i, f) && Pp(i, j) > 0.0) {
+                                    float p = Qgl(i, d - 1, e, f) * Qgr(d, e - 1, f + 1, j) *
+                                               EXP(-(score_at_penalty(d, j) + score_at_penalty(i, j)) / RT) / Qp(i, j) *
+                                               Pp(i, j);
+                                    Pgl(i, d - 1, e, f) += p;
+                                    Pgr(d, e - 1, f + 1, j) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Pgr recursion
+            for (int d = i + 1; d <= j - 3; ++d) {
+                for (int e = d + 2; e <= j - 1; ++e) {
+                    for (int f = e; f <= j - 1; ++f) {
+                        if (Pgr(i, d, e, j) > 0.0) {
+                            float p = Qgl(i, d, f, j) * Qz(e, f - 1) / Qgr(i, d, e, j) * Pgr(i, d, e, j);
+                            Pgl(i, d, f, j) += p;
+                            Pz(e, f - 1) += p;
+                            assert(!std::isnan(p));
+                        }
+                    }
+                }
+            }
+
+            // Pgl recursions
+            for (int d = i + 1; d <= j - 5; ++d) {
+                for (int f = d + 4; f <= j - 1; ++f) {
+                    if (allow_paired(d, f) && wc_pair(d, f)) {
+                        for (int e = d; e <= f - 2; ++e)    // f-3???
+                        {
+                            if (Pgl(i, e, f, j) > 0.0) {
+                                float p = Qg(i, d, f, j) * Qz(d + 1, e) *
+                                           EXP(-(score_pk_paired(1) + score_at_penalty(d, f)) / RT) / Qgl(i, e, f, j) *
+                                           Pgl(i, e, f, j);
+                                Pg(i, d, f, j) += p;
+                                Pz(d + 1, e) += p;
+                                Pbg(d, f) += p;    // Pbg inner gap-spanning base-pairing prob
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Pgrs recursion
+            for (int d = i + 1; d <= j - 10; ++d) {
+                for (int e = d + 4; e <= j - 6; ++e) {
+                    if (allow_paired(d, e)) {
+                        for (int f = e + 1; f <= j - 5; ++f) {
+                            if (allow_paired(i, f) && wc_pair(i, f) && Pgrs(i, d, e, j) > 0.0) {
+                                float p = Qg(i, d, e, f) * Qm(f + 1, j) *
+                                           EXP(-(score_multiloop_paired(1, true) + score_at_penalty(i, f)) / RT) /
+                                           Qgrs(i, d, e, j) * Pgrs(i, d, e, j);
+                                Pg(i, d, e, f) += p;
+                                Pm(f + 1, j) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Pgls recursion
+            for (int c = i + 5; c <= j - 6; ++c) {
+                if (allow_paired(c, j) && wc_pair(c, j)) {
+                    for (int d = c + 1; d <= j - 5; ++d) {
+                        for (int e = d + 4; e <= j - 1; ++e) {
+                            if (allow_paired(d, e) && Pgls(i, d, e, j) > 0.0) {
+                                float p = Qm(i, c - 1) * Qg(c, d, e, j) *
+                                           EXP(-(score_multiloop_paired(1, true) + score_at_penalty(c, j)) / RT) /
+                                           Qgls(i, d, e, j) * Pgls(i, d, e, j);
+                                Pm(i, c - 1) += p;
+                                Pg(c, d, e, j) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Pg recursion
+            fastiloops_pr(i, j, Qg, Qx, Qx2, Pg, Px, Px2);
+
+            if (allow_paired(i, j) && wc_pair(i, j)) {
+                // case 2: multiloop left
+                for (int d = i + 6; d <= j - 5; ++d) {
+                    for (int e = d + 4; e <= j - 1; ++e) {
+                        if (allow_paired(d, e) && wc_pair(d, e) && Pg(i, d, e, j) > 0.0) {
+                            float p =
+                            Qm(i + 1, d - 1) *
+                            EXP(
+                            -(
+                            score_multiloop(true) + score_multiloop_paired(2, true) + score_multiloop_unpaired(j - e - 1, true) +
+                            score_at_penalty(i, j) + score_at_penalty(d, e) + score_dangle(e + 1, j - 1)) /
+                            RT) /
+                            Qg(i, d, e, j) * Pg(i, d, e, j);
+                            Pm(i + 1, d - 1) += p;
+                            assert(!std::isnan(p));
+                        }
+                    }
+                }
+
+                // case 3: multiloop right
+                for (int d = i + 1; d <= j - 10; ++d) {
+                    for (int e = d + 4; e <= j - 6; ++e) {
+                        if (allow_paired(d, e) && wc_pair(d, e) && Pg(i, d, e, j) > 0.0) {
+                            float p =
+                            Qm(e + 1, j - 1) *
+                            EXP(
+                            -(
+                            score_multiloop(true) + score_multiloop_paired(2, true) + score_multiloop_unpaired(d - i - 1, true) +
+                            score_at_penalty(i, j) + score_at_penalty(d, e) + score_dangle(i + 1, d - 1)) /
+                            RT) /
+                            Qg(i, d, e, j) * Pg(i, d, e, j);
+                            Pm(e + 1, j - 1) += p;
+                            assert(!std::isnan(p));
+                        }
+                    }
+                }
+
+                // case 4: multiloop both sides
+                for (int d = i + 6; d <= j - 10; ++d) {
+                    for (int e = d + 4; e <= j - 6; ++e) {
+                        if (allow_paired(d, e) && wc_pair(d, e) && Pg(i, d, e, j) > 0.0) {
+                            float p =
+                            Qm(i + 1, d - 1) * Qm(e + 1, j - 1) *
+                            EXP(-(score_multiloop(true) + score_multiloop_paired(2, true) + score_at_penalty(i, j) + score_at_penalty(d, e)) / RT) /
+                            Qg(i, d, e, j) * Pg(i, d, e, j);
+                            Pm(i + 1, d - 1) += p;
+                            Pm(e + 1, j - 1) += p;
+                            assert(!std::isnan(p));
+                        }
+                    }
+                }
+
+                // case 5: interior loop + multi left
+                for (int d = i + 7; d <= j - 6; ++d) {
+                    for (int e = d + 4; e <= j - 2; ++e) {
+                        if (allow_paired(d, e)) {
+                            for (int f = e + 1; f <= j - 1; ++f) {
+                                if (Pg(i, d, e, j) > 0.0) {
+                                    float p = Qgls(i + 1, d, e, f) *
+                                               EXP(
+                                               -(
+                                               score_multiloop(true) + score_multiloop_paired(1, true) +
+                                               score_multiloop_unpaired(j - f - 1, true) + score_at_penalty(i, j) +
+                                               score_dangle(f + 1, j - 1)) /
+                                               RT) /
+                                               Qg(i, d, e, j) * Pg(i, d, e, j);
+                                    Pgls(i + 1, d, e, f) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+                        }
+                    }
+                }
+
+                // case 6: interior loop + multi right
+                for (int d = i + 2; d <= j - 11; ++d) {
+                    for (int e = d + 4; e <= j - 7; ++e) {
+                        if (allow_paired(d, e)) {
+                            for (int c = i + 1; c <= d - 1; ++c) {
+                                if (Pg(i, d, e, j) > 0.0) {
+                                    float p = Qgrs(c, d, e, j - 1) *
+                                               EXP(
+                                               -(
+                                               score_multiloop(true) + score_multiloop_paired(1, true) +
+                                               score_multiloop_unpaired(c - i - 1, true) + score_at_penalty(i, j) +
+                                               score_dangle(i + 1, c - 1)) /
+                                               RT) /
+                                               Qg(i, d, e, j) * Pg(i, d, e, j);
+                                    Pgrs(c, d, e, j - 1) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+                        }
+                    }
+                }
+
+                // case 7: interior loop + multi both sides
+                for (int d = i + 7; d <= j - 11; ++d) {
+                    for (int e = d + 4; e <= j - 7; ++e) {
+                        if (allow_paired(d, e)) {
+                            for (int c = i + 6; c <= d - 1; ++c) {
+                                if (Pg(i, d, e, j) > 0.0) {
+                                    float p =
+                                    Qm(i + 1, c - 1) * Qgrs(c, d, e, j - 1) *
+                                    EXP(-(score_multiloop(true) + score_multiloop_paired(1, true) + score_at_penalty(i, j)) / RT) /
+                                    Qg(i, d, e, j) * Pg(i, d, e, j);
+                                    Pm(i + 1, c - 1) += p;
+                                    Pgrs(c, d, e, j - 1) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+
+            // Pbg outer gap-spanning base-pairing prob
+            for (int d = i + 1; d <= j - 5; ++d)
+                for (int e = d + 4; e <= j - 1; ++e) Pbg(i, j) += Pg(i, d, e, j);
+
+            // Pb recursion
+            if (allow_paired(i, j)) {
+                for (int d = i + 1; d <= j - 5; ++d)    // all possible rightmost pairs d-e
+                {
+                    for (int e = d + 4; e <= j - 1; ++e) {
+                        if (allow_paired(d, e)) {
+                            if (Pb(i, j) > 0.0) {
+                                float p = Qb(d, e) * EXP(-score_interior(i, d, e, j, false) / RT) / Qb(i, j) * Pb(i, j);
+                                Pb(d, e) += p;
+                                assert(!std::isnan(p));
+
+                                if (d >= i + 6 && wc_pair(d, e) && wc_pair(i, j)) {
+                                    float p = Qm(i + 1, d - 1) * Qb(d, e) *
+                                               EXP(
+                                               -(
+                                               score_multiloop(false) + score_multiloop_paired(2, false) +
+                                               score_multiloop_unpaired(j - e - 1, false) + score_at_penalty(i, j) +
+                                               score_at_penalty(d, e) + score_dangle(e + 1, j - 1)) /
+                                               RT) /
+                                               Qb(i, j) * Pb(i, j);
+                                    Pm(i + 1, d - 1) += p;
+                                    Pb(d, e) += p;
+                                    assert(!std::isnan(p));
+                                }
+                            }
+                        }
+                    }
+                }
+
+                if (wc_pair(i, j)) {
+                    for (int d = i + 1; d <= j - 6; ++d)    // all possible rightmost pseudoknots filling [d,e]
+                    {
+                        for (int e = d + 5; e <= j - 1; ++e) {
+                            if (Pb(i, j) > 0.0) {
+                                float p;
+                                p = Qp(d, e) *
+                                    EXP(
+                                    -(
+                                    score_multiloop(false) + score_pk_multiloop() + score_multiloop_paired(3, false) +
+                                    score_multiloop_unpaired(j - e - 1 + d - i - 1, false) + score_at_penalty(i, j) +
+                                    score_dangle(e + 1, j - 1) + score_dangle(i + 1, d - 1)) /
+                                    RT) /
+                                    Qb(i, j) * Pb(i, j);
+                                Pp(d, e) += p;
+                                assert(!std::isnan(p));
+
+                                p = Qm(i + 1, d - 1) * Qp(d, e) *
+                                    EXP(
+                                    -(
+                                    score_multiloop(false) + score_pk_multiloop() + score_multiloop_paired(3, false) +
+                                    score_multiloop_unpaired(j - e - 1, false) + score_at_penalty(i, j) +
+                                    score_dangle(e + 1, j - 1)) /
+                                    RT) /
+                                    Qb(i, j) * Pb(i, j);
+                                Pm(i + 1, d - 1) += p;
+                                Pp(d, e) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+void Nupack::fastiloops_pr(int i, int j, DPtable4& Qg, DPtableX& Qx, DPtableX& Qx2, DPtable4& Pg, DPtableX& Px, DPtableX& Px2)
+{
+    int l = j - i + 1;
+
+    if (allow_paired(i, j)) {
+        for (int d = i + 1; d <= j - 5; ++d) {
+            for (int e = d + 4; e <= j - 1; ++e) {
+                if (allow_paired(d, e)) {
+                    // Add small inextensible interior loops to Qg as special cases
+                    for (int l1 = 0; l1 <= std::min(3, d - i - 2); ++l1) {
+                        int c = i + l1 + 1;
+                        for (int l2 = 0; l2 <= std::min(3, j - e - 2); ++l2) {
+                            int f = j - l2 - 1;
+                            if (allow_paired(c, f) && Pg(i, d, e, j) > 0.0) {
+                                float p = Qg(c, d, e, f) * EXP(-score_interior(i, c, f, j, true) / RT) /
+                                           Qg(i, d, e, j) * Pg(i, d, e, j);
+                                Pg(c, d, e, f) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                    // Add bulge loops and large asymmetric loops as special cases
+                    for (int l1 = 0; l1 <= std::min(3, d - i - 2); ++l1)    // cases l1=0,1,2,3, l2>=4
+                    {
+                        int c = i + l1 + 1;
+                        for (int l2 = 4; l2 <= j - e - 2; ++l2) {
+                            int f = j - l2 - 1;
+                            if (allow_paired(c, f) && Pg(i, d, e, j) > 0.0) {
+                                float p = Qg(c, d, e, f) * EXP(-score_interior(i, c, f, j, true) / RT) /
+                                           Qg(i, d, e, j) * Pg(i, d, e, j);
+                                Pg(c, d, e, f) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                    for (int l2 = 0; l2 <= std::min(3, j - e - 2); ++l2) {
+                        int f = j - l2 - 1;
+                        for (int l1 = 4; l1 <= d - i - 2; ++l1) {
+                            int c = i + l1 + 1;
+                            if (allow_paired(c, f) && Pg(i, d, e, j) > 0.0) {
+                                float p = Qg(c, d, e, f) * EXP(-score_interior(i, c, f, j, true) / RT) /
+                                           Qg(i, d, e, j) * Pg(i, d, e, j);
+                                Pg(c, d, e, f) += p;
+                                assert(!std::isnan(p));
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    // Add cases that are at an end with l1>=4, l2>=4
+    if ((i == 0 || j == N - 1) && l >= 17) {
+        for (int d = i + 6; d <= j - 10; ++d) {
+            for (int e = d + 4; e <= j - 6; ++e) {
+                if (allow_paired(d, e)) {
+                    for (int c = i + 5; c <= d - 1; ++c) {
+                        for (int f = e + 1; f <= j - 5; ++f) {
+                            if (allow_paired(c, f)) {
+                                int l1 = c - i - 1;
+                                int l2 = j - f - 1;
+                                int s  = l1 + l2;
+                                Qx(i, d, e, s) +=
+                                Qg(c, d, e, f) *
+                                EXP(-(score_interior_asymmetry(l1, l2) + score_interior_mismatch(f, c, f + 1, c - 1)) / RT);
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    // Use Qx to finish calculation of Px
+    if (allow_paired(i, j)) {
+        for (int d = i + 1; d <= j - 5; ++d) {
+            for (int e = d + 4; e <= j - 1; ++e) {
+                if (allow_paired(d, e)) {
+                    for (int s = 8; s <= l - 9; ++s) {
+                        float p = Qx(i, d, e, s) * EXP(-score_interior_mismatch(i, j, i + 1, j - 1) / RT) /
+                                   Qg(i, d, e, j) * Pg(i, d, e, j);
+                        Px(i, d, e, s) += p;
+                        assert(!std::isnan(p));
+                    }
+                }
+            }
+        }
+    }
+
+    // Calculate Pg contribution using Qx and Px
+    if (l >= 17) {
+        for (int d = i + 6; d <= j - 10; ++d) {
+            for (int e = d + 4; e <= j - 6; ++e) {
+                if (allow_paired(d, e)) {
+                    int l1 = 4;    // explicitly add in terms for l1=4, l2>=4
+                    int c  = i + l1 + 1;
+                    for (int l2 = 4; l2 <= j - e - 2; ++l2) {
+                        int s = l1 + l2;
+                        int f = j - l2 - 1;
+                        if (allow_paired(c, f) && Qx(i, d, e, s) > 0.0) {
+                            float temp =
+                            Qg(c, d, e, f) *
+                            EXP(-(score_interior_asymmetry(l1, l2) + score_interior_mismatch(f, c, f + 1, c - 1)) / RT);
+                            float p = temp / Qx(i, d, e, s) * Px(i, d, e, s);
+                            Pg(c, d, e, f) += p;
+                            Px(i, d, e, s) -= p;
+                            assert(!std::isnan(p));
+                            if (temp > Qx(i, d, e, s)) {
+                                temp      = 0.0;
+                                int l1min = 5;
+                                int l2min = 4;
+                                for (int c = i + l1min + 1; c <= d - 1; ++c) {
+                                    int f = c - i + j - 3;
+                                    if (j - f - 1 > l2min && f >= e + 1 && allow_paired(c, f)) {
+                                        temp += Qg(c, d, e, f) * EXP(-score_interior(i, j, c, f, true) / RT);
+                                    }
+                                }
+                                Qx(i, d, e, s) = temp;
+                            } else {
+                                Qx(i, d, e, s) -= temp;
+                            }
+                        }
+                    }
+
+                    if (d >= i + 7) {
+                        int l2 = 4;    // explicitly add in terms of l1>=5, l2=4
+                        int f  = j - l2 - 1;
+                        for (int l1 = 5; l1 <= d - i - 2; ++l1) {
+                            int s = l1 + l2;
+                            int c = i + l1 + 1;
+                            if (allow_paired(c, f) && Qx(i, d, e, s) > 0.0) {
+                                float temp =
+                                Qg(c, d, e, f) *
+                                EXP(-(score_interior_asymmetry(l1, l2) + score_interior_mismatch(f, c, f + 1, c - 1)) / RT);
+                                float p = temp / Qx(i, d, e, s) * Px(i, d, e, s);
+                                Pg(c, d, e, f) += p;
+                                Px(i, d, e, s) -= p;
+                                assert(!std::isnan(p));
+                                if (temp > Qx(i, d, e, s)) {
+                                    temp      = 0.0;
+                                    int l1min = 5;
+                                    int l2min = 5;
+                                    for (int c = i + l1min + 1; c <= d - 1; ++c) {
+                                        int f = c - i + j - 4;
+                                        if (j - f - 1 > l2min && f >= e + 1 && allow_paired(c, f)) {
+                                            temp += Qg(c, d, e, f) * EXP(-score_interior(i, j, c, f, true) / RT);
+                                        }
+                                    }
+                                    Qx(i, d, e, s) = temp;
+                                } else {
+                                    Qx(i, d, e, s) -= temp;
+                                }
+                            }
+                        }
+                    }
+                }
+
+                // Store partial values for Qx2 and Px2
+                for (int s = 10; s <= l - 9; ++s) {
+                    Qx2(i + 1, d, e, s - 2) = Qx(i, d, e, s) * EXP(-(score_loop(s + 2) - score_loop(s)) / RT);
+                    Px2(i + 1, d, e, s - 2) = Px(i, d, e, s);
+                }
+            }
+        }
+    }
+}
+
+void Nupack::get_posterior(vector<float>& bp1, vector<float>& bp2, vector<int>& offset) const
+{
+    bp1.resize((N + 1) * (N + 2) / 2);
+    bp2.resize((N + 1) * (N + 2) / 2);
+    offset.resize(N + 1);
+    for (int i = 0; i <= N; ++i) offset[i] = i * ((N + 1) + (N + 1) - i - 1) / 2;
+    for (int i = 0; i != N - 1; ++i)
+        for (int j = i + 1; j != N; ++j) {
+            bp1[offset[i + 1] + (j + 1)] = Pb(i, j);
+            bp2[offset[i + 1] + (j + 1)] = Pbg(i, j);
+        }
+}
+
+void Nupack::get_posterior(vector<float>& bp, vector<int>& offset) const
+{
+    bp.resize((N + 1) * (N + 2) / 2);
+    offset.resize(N + 1);
+    for (int i = 0; i <= N; ++i) offset[i] = i * ((N + 1) + (N + 1) - i - 1) / 2;
+    for (int i = 0; i != N - 1; ++i)
+        for (int j = i + 1; j != N; ++j) bp[offset[i + 1] + (j + 1)] = Pb(i, j) + Pbg(i, j);
+}
+
+energy_t Nupack::score_hairpin(int i, int j) const
+{
+    energy_t e     = 0.0;
+    bool     polyC = true;
+    for (int k = i + 1; k < j; ++k) {
+        if (seq[k] != BASE_C) {
+            polyC = false;
+            break;
+        }
+    }
+
+    int size = j - i - 1;
+
+    assert(size >= 3);
+    assert(allow_paired(i, j));
+
+
+    e += size <= 30 ? hairpin37[size - 1] : hairpin37[30 - 1] + loop_greater30 * LOG(size / 30.0);
+
+    if (size == 3) {
+        e += score_at_penalty(i, j);
+        e += triloop37[seq[i] - 1][seq[i + 1] - 1][seq[i + 2] - 1][seq[j - 1] - 1][seq[j] - 1];
+        if (polyC) e += polyC_penalty;
+        if (seq[i + 1] == BASE_G && seq[i + 2] == BASE_G && seq[j - 1] == BASE_G) e += hairpin_GGG;
+    } else if (size == 4) {
+        e += tloop37[seq[i] - 1][seq[i + 1] - 1][seq[i + 2] - 1][seq[j - 2] - 1][seq[j - 1] - 1][seq[j] - 1];
+        e += mismatch_hairpin37[seq[i + 1] - 1][seq[j - 1] - 1][pair_type(i, j)];
+        if (polyC) e += polyC_slope * size + polyC_int;
+    } else /*if (size>4)*/
+    {
+        e += mismatch_hairpin37[seq[i + 1] - 1][seq[j - 1] - 1][pair_type(i, j)];
+        if (polyC) e += polyC_slope * size + polyC_int;
+    }
+    return e;
+}
+
+energy_t Nupack::score_loop(int l) const
+{
+    return l <= 30 ? interior37[l - 1] : interior37[30 - 1] + loop_greater30 * LOG(l / 30.0);
+}
+
+energy_t Nupack::score_interior(int i, int h, int m, int j, bool pk) const
+{
+    int      l1   = h - i - 1;
+    int      l2   = j - m - 1;
+    int      size = l1 + l2;
+    energy_t e    = 0;
+
+    // helix
+    if (size == 0) {
+        return stack37[pair_type(i, j)][pair_type(h, m)] * (pk ? pk_stack_span : 1.0);
+    }
+
+    // bulge
+    else if (l1 == 0 || l2 == 0) {
+        e += size <= 30 ? bulge37[size - 1] : bulge37[30 - 1] + loop_greater30 * LOG(size / 30.0);
+
+        if (l1 + l2 == 1)    // single bulge...treat as a stacked region
+        {
+            e += stack37[pair_type(i, j)][pair_type(h, m)];
+            e -= salt_correction;
+        } else {
+            e += score_at_penalty(i, j);
+            e += score_at_penalty(h, m);
+        }
+    }
+
+    // interior loop
+    else if (l1 > 0 && l2 > 0) {
+        int asymmetry = std::abs(l1 - l2);
+        if (asymmetry > 1 || size > 4) {
+            e += score_interior_asymmetry(l1, l2);
+            if (l1 > 1 && l2 > 1) {
+                e += score_interior_mismatch(m, h, m + 1, h - 1);
+                e += score_interior_mismatch(i, j, i + 1, j - 1);
+            } else if (l1 == 1 || l2 == 1) {
+                e += score_interior_mismatch(m, h);
+                e += score_interior_mismatch(i, j);
+            } else {
+                assert(!"unclassified interior loop");
+                exit(1);
+            }
+        } else if (l1 == 1 && l2 == 1)
+            e += int11_37[pair_type(i, j)][pair_type(h, m)][seq[i + 1] - 1][seq[j - 1] - 1];
+        else if (l1 == 2 && l2 == 2)
+            e += int22_37[pair_type(i, j)][pair_type(h, m)][seq[i + 1] - 1][seq[j - 1] - 1][seq[i + 2] - 1][seq[j - 2] - 1];
+        else if (l1 == 1 && l2 == 2)
+            e += int21_37[pair_type(i, j)][seq[j - 2] - 1][seq[i + 1] - 1][pair_type(h, m)][seq[j - 1] - 1];
+        else if (l1 == 2 && l2 == 1)
+            e += int21_37[pair_type(m, h)][seq[i + 1] - 1][seq[j - 1] - 1][pair_type(j, i)][seq[i + 2] - 1];
+        else {
+            assert(!"error in tabulated interior loop");
+            exit(1);
+        }
+    } else {
+        assert(!"improperly classifed interior loop");
+        exit(1);
+    }
+    return e * (pk ? pk_interior_span : 1.0);
+}
+
+energy_t Nupack::score_interior_mismatch(int i, int j, int k, int l) const
+{
+    return mismatch_interior37[seq[k] - 1][seq[l] - 1][pair_type(i, j)];
+}
+
+energy_t Nupack::score_interior_mismatch(int i, int j) const
+{
+    return mismatch_interior37[BASE_N][BASE_N][pair_type(i, j)];
+}
+
+energy_t Nupack::score_interior_asymmetry(int l1, int l2) const
+{
+    energy_t e         = 0.0;
+    int      size      = l1 + l2;
+    int      asymmetry = std::abs(l1 - l2);
+    e += size <= 30 ? interior37[size - 1] : interior37[30 - 1] + loop_greater30 * LOG(size / 30.0);
+
+    // asymmetry penalty
+    e += std::min(max_asymmetry, asymmetry * asymmetry_penalty[std::min(4, std::min(l1, l2)) - 1]);
+
+    return e;
+}
+
+energy_t Nupack::score_multiloop(bool pk) const { return pk ? multiloop_penalty_pk : multiloop_penalty; }
+
+energy_t Nupack::score_multiloop_paired(int n, bool pk) const
+{
+    return (pk ? multiloop_paired_penalty_pk : multiloop_paired_penalty) * n;
+}
+
+energy_t Nupack::score_multiloop_unpaired(int n, bool pk) const
+{
+    return (pk ? multiloop_unpaired_penalty_pk : multiloop_unpaired_penalty) * n;
+}
+
+energy_t Nupack::score_at_penalty(int i, int j) const
+{
+    return pair_type(i, j) == PAIR_AU || pair_type(i, j) == PAIR_UA ? at_penalty : 0;
+}
+
+energy_t Nupack::score_dangle(int i, int j) const
+{
+    energy_t d5 = 0.0, d3 = 0.0;
+
+    // if( DANGLETYPE != 2) {
+    if ((j == i - 1) || (j == -1 && i > 0)) {
+        return 0.0;
+    }
+    if ((j == -1 && i > 0) || (j == i - 1 && (i == 0 || j == N - 1))) return 0.0;
+    if (j != N - 1) d3 = dangle3_37[3 - pair_type(j + 1)][seq[j] - 1];
+    if (i != 0) d5 = dangle5_37[pair_type(i - 1)][seq[i] - 1];
+    if (i == j && i != 0 && j != N - 1 /* && DANGLETYPE!=2 */)
+        return std::min(d3, d5);
+    else
+        return d3 + d5;
+}
+
+inline energy_t Nupack::score_pk() const { return pk_penalty; }
+inline energy_t Nupack::score_pk_multiloop() const { return pk_multiloop_penalty; }
+inline energy_t Nupack::score_pk_pk() const { return pk_pk_penalty; }
+inline energy_t Nupack::score_pk_paired(int n) const { return pk_paired_penalty * n; }
+inline energy_t Nupack::score_pk_unpaired(int n) const { return pk_unpaired_penalty * n; }
+inline energy_t Nupack::score_pk_band(int n) const { return pk_band_penalty * n; }

+/*
+ * $Id$
+ *
+ * Copyright (C) 2010 Kengo Sato
+ *
+ * This file comes from IPknot.
+ *
+ */
+
+#include <boost/multi_array.hpp>
+#include <string>
+#include <vector>
+#include <iostream>
+
+using std::string;
+using std::vector;
+
+#define kB 0.00198717              // Boltzmann constant in kcal/mol/K
+#define ZERO_C_IN_KELVIN 273.15    // Zero degrees C in Kelvin
+#define AVOGADRO 6.022e23          // Avogadro's number
+
+typedef float energy_t;
+
+class DPtable2
+{
+  public:
+    DPtable2() : V_(), N_(0) {}
+    void resize(int n)
+    {
+        N_ = n;
+        V_.resize(N_ * (N_ + 1) / 2 + (N_ + 1));
+    }
+    void          fill(const float& v) { std::fill(V_.begin(), V_.end(), v); }
+    float&       operator()(int i, int j) { return V_[index(i, j)]; }
+    const float& operator()(int i, int j) const { return V_[index(i, j)]; }
+
+  private:
+    int index(int i, int j) const
+    {
+        assert(j <= N_);
+        return j == i - 1 ? N_ * (N_ + 1) / 2 + i : i * N_ + j - i * (1 + i) / 2;
+    }
+    std::vector<float> V_;
+    int                 N_;
+};
+
+class DPtable4
+{
+  public:
+    DPtable4() : V_(), N_(0) {}
+    void resize(int n)
+    {
+        N_ = n;
+        std::cout << V_.max_size() << " - " << N_ << " - " <<  sizeof(float) * static_cast<unsigned long>(N_) * (N_ - 1) * (N_ - 2) * (N_ - 3) / 2 / 3 / 4 << std::endl;
+        V_.resize(static_cast<unsigned long>(N_) * (N_ - 1) * (N_ - 2) * (N_ - 3) / 2 / 3 / 4); // This number can be HUGE
+        std::cout << "c'est toi qui bad_allocque ?" << std::endl;         
+    }
+    void          fill(const float& v) { std::fill(V_.begin(), V_.end(), v); }
+    float&       operator()(int i, int d, int e, int j) { return V_[index(i, d, e, j)]; }
+    const float& operator()(int i, int d, int e, int j) const { return V_[index(i, d, e, j)]; }
+
+  private:
+    int index(int h, int r, int m, int s) const
+    {
+        int n  = N_;
+        int h2 = h * h;
+        int h3 = h2 * h;
+        int h4 = h3 * h;
+        int m2 = m * m;
+        int n2 = n * n;
+        int n3 = n2 * n;
+        int r2 = r * r;
+        int r3 = r2 * r;
+        assert(h <= r);
+        assert(r <= m);
+        assert(m <= s);
+        assert(s <= N_);
+        return (h == r && m == s) ? V_.size() - 1 :
+                                    (
+                                    -24 - 50 * h - 35 * h2 - 10 * h3 - h4 - 36 * m - 12 * m2 + 12 * n + 70 * h * n +
+                                    30 * h2 * n + 4 * h3 * n + 24 * m * n - 12 * n2 - 30 * h * n2 - 6 * h2 * n2 + 4 * h * n3 +
+                                    44 * r - 48 * n * r + 12 * n2 * r + 24 * r2 - 12 * n * r2 + 4 * r3 + 24 * s) /
+                                    24;
+    }
+    std::vector<float> V_;
+    int                 N_;
+};
+
+class DPtableX
+{
+  public:
+    DPtableX() : V_(), N_(0), D_(0) {}
+    void resize(int d, int n)
+    {
+        N_         = n;
+        D_         = d;
+        int max_sz = 0;
+        for (int i = d; i < d + 3; ++i) max_sz = std::max(max_sz, (N_ - i) * (i - 5) * (i - 1) * (i - 2) / 2);
+        V_.resize(max_sz);
+    }
+    void          fill(const float& v) { std::fill(V_.begin(), V_.end(), v); }
+    float&       operator()(int i, int d, int e, int s) { return V_[index(i, d, e, s)]; }
+    const float& operator()(int i, int d, int e, int s) const { return V_[index(i, d, e, s)]; }
+    void          swap(DPtableX& x)
+    {
+        std::swap(V_, x.V_);
+        std::swap(N_, x.N_);
+        std::swap(D_, x.D_);
+    }
+
+  private:
+    int index(int i, int h1, int m1, int s) const
+    {
+        int d      = D_;
+        int d1d2   = (d - 1) * (d - 2);
+        int d5     = d - 5;
+        int h1_i_1 = h1 - i - 1;
+        assert(i + d < N_);
+        assert(d - 6 >= s);
+        assert(i < h1);
+        return i * d5 * d1d2 / 2 + s * d1d2 / 2 + h1_i_1 * (d - 1) - h1_i_1 * (h1 - i) / 2 + m1 - h1 - 1;
+    }
+
+    std::vector<float> V_;
+    int                 N_;
+    int                 D_;
+};
+
+class Nupack
+{
+  public:
+    Nupack();
+    void        load_sequence(const string& s);
+    void        load_parameters_fm363(const vector<float>& v);
+    void        load_default_parameters(/*int which*/);
+    bool        load_parameters(const char* filename);
+    void        dump_parameters(std::ostream& os) const;
+    float calculate_partition_function();
+    void        calculate_posterior();
+    void        get_posterior(vector<float>& bp, vector<int>& offset) const;
+    void        get_posterior(vector<float>& bp1, vector<float>& bp2, vector<int>& offset) const;
+
+  private:
+    void fastiloops(int i, int j, DPtable4& Qg, DPtableX& Qx, DPtableX& Qx2);
+    void fastiloops_pr(int i, int j, DPtable4& Qg, DPtableX& Qx, DPtableX& Qx2, DPtable4& Pg, DPtableX& Px, DPtableX& Px2);
+    energy_t score_hairpin(int i, int j) const;
+    energy_t score_loop(int l) const;
+    energy_t score_interior(int i, int d, int e, int j, bool pk) const;
+    energy_t score_interior_mismatch(int i, int j) const;
+    energy_t score_interior_mismatch(int i, int j, int k, int l) const;
+    energy_t score_interior_asymmetry(int l1, int l2) const;
+    energy_t score_multiloop(bool pk) const;
+    energy_t score_multiloop_paired(int n, bool pk) const;
+    energy_t score_multiloop_unpaired(int n, bool pk) const;
+    energy_t score_at_penalty(int i, int j) const;
+    energy_t score_dangle(int i, int j) const;
+    energy_t score_pk() const;
+    energy_t score_pk_multiloop() const;
+    energy_t score_pk_pk() const;
+    energy_t score_pk_paired(int n) const;
+    energy_t score_pk_unpaired(int n) const;
+    energy_t score_pk_band(int n) const;
+    int      base(char x) const;
+    bool     allow_paired(int i, int j) const;
+    bool     wc_pair(int i, int j) const;
+    int      pair_type(int i, int j) const;
+    int      pair_type(int i) const;
+
+    vector<int>                base_map;
+    boost::multi_array<int, 2> pair_map;
+    vector<int>                seq;
+    int                        N;
+    float                      RT;
+    DPtable2                   Q;
+    DPtable2                   Qb;
+    DPtable2                   Qm;
+    DPtable2                   Qp;
+    DPtable2                   Qz;
+    DPtable4                   Qg;
+    DPtable4                   Qgl;
+    DPtable4                   Qgr;
+    DPtable4                   Qgls;
+    DPtable4                   Qgrs;
+    DPtable2                   P;
+    DPtable2                   Pb;
+    DPtable2                   Pm;
+    DPtable2                   Pp;
+    DPtable2                   Pz;
+    DPtable2                   Pbg;
+    DPtable4                   Pg;
+    DPtable4                   Pgl;
+    DPtable4                   Pgr;
+    DPtable4                   Pgls;
+    DPtable4                   Pgrs;
+
+    // energy parameters
+    energy_t hairpin37[30];
+    energy_t bulge37[30];
+    energy_t interior37[30];
+    energy_t stack37[6][6];
+    energy_t int11_37[6][6][4][4];
+    energy_t int21_37[6][4][4][6][4];
+    energy_t int22_37[6][6][4][4][4][4];
+    energy_t dangle3_37[6][4];
+    energy_t dangle5_37[6][4];
+    energy_t triloop37[4][4][4][4][4];
+    energy_t tloop37[4][4][4][4][4][4];
+    energy_t mismatch_hairpin37[4][4][6];
+    energy_t mismatch_interior37[4][4][6];
+    energy_t asymmetry_penalty[4];
+    energy_t polyC_penalty, polyC_slope, polyC_int;
+    energy_t at_penalty;
+    energy_t multiloop_penalty;             // alpha1
+    energy_t multiloop_paired_penalty;      // alpha2
+    energy_t multiloop_unpaired_penalty;    // alpha3
+    energy_t pk_penalty;                    // beta1
+    energy_t pk_multiloop_penalty;          // beta1m
+    energy_t pk_pk_penalty;                 // beta1p
+    energy_t pk_paired_penalty;             // beta2
+    energy_t pk_unpaired_penalty;           // beta3
+    energy_t pk_band_penalty;
+    energy_t pk_stack_span;
+    energy_t pk_interior_span;
+    energy_t multiloop_penalty_pk;
+    energy_t multiloop_paired_penalty_pk;
+    energy_t multiloop_unpaired_penalty_pk;
+    energy_t max_asymmetry;
+    energy_t salt_correction;
+    energy_t loop_greater30;
+    energy_t hairpin_GGG;
+    float    intermolecular_initiation;
+};

+#include "rna.h"
+#include "nupack.h"
+#include <iostream>
+#include <string>
+#include <utility>
+#include <vector>
+
+using std::cout, std::cerr, std::endl;
+
+RNA::RNA(string name, string seq)
+{
+    if (!check_seq(seq)) {
+        cerr << "Unknown chars in input sequence. Please restrict to ACGTU." << endl;
+        exit(EXIT_FAILURE);
+    }
+    name_ = name;
+    seq_  = seq;
+    format();
+    n_ = seq_.size();
+    cout << "\t>formatted sequence" << endl;
+
+    /*define type_*/
+    type_ = vector<vector<int>>(n_, vector<int>(n_));
+    for (int i = 0; i < n_; i++) {
+        for (int j = 0; j < n_; j++) {
+            if (i < j) {
+                std::stringstream ss;
+                ss << seq_[i] << seq_[j];
+                string str = ss.str();
+                if (str.compare("AU") == 0) {
+                    type_[i][j] = 1;
+                } else if (str.compare("CG") == 0) {
+                    type_[i][j] = 2;
+
+                } else if (str.compare("GC") == 0) {
+                    type_[i][j] = 3;
+                } else if (str.compare("GU") == 0) {
+                    type_[i][j] = 4;
+                } else if (str.compare("UG") == 0) {
+                    type_[i][j] = 5;
+                } else if (str.compare("UA") == 0) {
+                    type_[i][j] = 6;
+                } else {
+                    type_[i][j] = 0;
+                }
+            } else {
+                type_[i][j] = 0;
+            }
+        }
+    }
+    nBP_ = type_.size();
+
+    /*define coord_*/
+    for (int i = 0; i < n_; i++) {
+        for (int j = 0; j < n_; j++) {
+            if (i < j and type_[i][j] > 0) {
+                if (i != 0 and i != n_ and j != 0 and j != n_) {
+                    if (type_[i - 1][j + 1] > 0 or type_[i + 1][j - 1] > 0) {
+                        coord_.push_back(std::make_pair(i, j));
+                    }
+                } else if (i == 0 or j == n_) {
+                    if (type_[i + 1][j - 1] > 0) {
+                        coord_.push_back(std::make_pair(i, j));
+                    }
+                }
+            }
+        }
+    }
+
+
+    /*define pij_*/
+    vector<float> bp;
+    vector<int>   offset;
+    Nupack        nu;
+    // nu.load_parameters("rna1999.dG");
+    nu.load_default_parameters();
+    cout << "\t>default parameters loaded (Serra and Turner, 1995)" << endl;
+    nu.load_sequence(seq_);
+    cout << "\t>computing pairing probabilities..." << endl;
+    try {
+        nu.calculate_partition_function();
+    } catch (std::exception& e) {
+        cerr << e.what() << endl;
+        exit(EXIT_FAILURE);
+    }
+    nu.calculate_posterior();
+    nu.get_posterior(bp, offset);
+
+    pij_ = vector<vector<float>>(n_, vector<float>(n_));
+    for (int i = 1; i <= n_; i++) {
+        for (int j = 1; j <= n_; j++) {
+            pij_[i - 1][j - 1] = bp[offset[i] + j];
+        }
+    }
+    cout << "\t>pairing probabilities defined" << endl;
+}
+
+int RNA::find_coord(pair<int, int> p)
+{
+    vector<pair<int, int>>::iterator it = find(coord_.begin(), coord_.end(), p);
+    int                              r  = -1;
+    if (it != coord_.end()) r = distance(coord_.begin(), it);
+    return r;
+}
+
+bool RNA::check_seq(string seq)    // Checks if the sequences only contains ACGUT.
+{
+    bool res = true;
+    for (unsigned int i = 0; i < seq.size(); i++) {
+        if (seq[i] != 'A' and seq[i] != 'U' and seq[i] != 'C' and seq[i] != 'G' and seq[i] != 'T') {
+            res = false;
+            break;
+        }
+    }
+    return res;
+}
+
+void RNA::format()
+{
+    for (unsigned int i = 0; i < seq_.size(); i++) {
+        seq_[i] = toupper(seq_[i]);
+        if (seq_[i] == 'T') {
+            seq_[i] = 'U';
+            break;
+        }
+    }
+}

+
+#ifndef DEF_RNA
+#define DEF_RNA
+
+#include <map>
+#include <string>
+#include <vector>
+
+using std::pair, std::string, std::vector, std::map;
+
+typedef struct Comp_ {
+    pair<uint, uint> pos;
+    int              score;
+    size_t           k;
+    Comp_(pair<int, int> p, int s) : pos(p), score(s) { k = 1 + pos.second - pos.first; }
+} Component;
+typedef struct {
+    string            atlas_id;
+    vector<Component> comp;
+    bool              reversed;
+} Motif;
+
+class RNA
+{
+  public:
+    RNA();
+    RNA(string name, string seq);
+
+    int                    get_n_();
+    string                 get_name_();
+    string                 get_seq_();
+    vector<vector<int>>    get_type_();
+    int                    get_type(int i, int j);
+    int                    get_type(int i);
+    vector<pair<int, int>> get_coord_();
+    pair<int, int>         get_coord(int i);
+    int                    get_coordF(int i);
+    int                    get_coordS(int i);
+    int                    find_coord(pair<int, int>);
+    vector<vector<float>>  get_pij_();
+    float                  get_pij(int i, int j);
+    float                  get_pij(int i);
+    int                    get_err_();
+    uint                   get_RNA_length() const;
+
+    bool check_seq(string seq);
+    void format();
+
+  private:
+    string                          name_;  /*name of the rna*/
+    string                          seq_;   /*sequence of the rna*/
+    int                             n_;     /*length of the rna*/
+    vector<vector<int>>             type_;  /*vector of base pair types*/
+    vector<pair<int, int>>          coord_; /*vector of base pair coordinates*/
+    vector<vector<float>>           pij_;   /*vector of probabilities*/
+    uint                            nBP_;   /*number of possible base pair*/
+};
+
+inline int                    RNA::get_n_() { return n_; }
+inline string                 RNA::get_name_() { return name_; }
+inline string                 RNA::get_seq_() { return seq_; }
+inline vector<vector<int>>    RNA::get_type_() { return type_; }
+inline int                    RNA::get_type(int i, int j) { return type_[i][j]; }
+inline int                    RNA::get_type(int i) { return type_[get_coord(i).first][get_coord(i).second]; }
+inline vector<pair<int, int>> RNA::get_coord_() { return coord_; }
+inline pair<int, int>         RNA::get_coord(int i) { return coord_[i]; }
+inline int                    RNA::get_coordF(int i) { return coord_[i].first; }
+inline int                    RNA::get_coordS(int i) { return coord_[i].second; }
+inline vector<vector<float>>  RNA::get_pij_() { return pij_; }
+inline float                  RNA::get_pij(int i, int j) { return pij_[i][j]; }
+inline float                  RNA::get_pij(int i) { return pij_[get_coord(i).first][get_coord(i).second]; }
+inline uint                   RNA::get_RNA_length() const { return nBP_; }
+
+#endif

+// These parameter values are extracted from the larger files rna1995.dG 
+// Serra and Turner, 1995 
+// >All values represent delta G in units of decacal/mol (0.01 kcal/mol)
+
+struct sp_loops {
+    const char* s;
+    int         e;
+};
+
+static sp_loops triloops[] = {{"AAAAU", 0}, {nullptr, 0}};
+
+static sp_loops tetraloops[] = {
+{"AAUUUU", -200}, 
+{"ACUUGU", -200}, 
+{"AGAAAU", -200}, 
+{"AGAGAU", -200}, 
+{"AGCAAU", -200}, 
+{"AGCGAU", -200}, 
+{"AGGAAU", -200}, 
+{"AGUAAU", -200}, 
+{"AGUGAU", -200}, 
+{"AUACGU", -200}, 
+{"AUCCGU", -200}, 
+{"AUUCGU", -200}, 
+{"AUUUAU", -200}, 
+{"CAUUUG", -200}, 
+{"CCUUGG", -200}, 
+{"CGAAAG", -200}, 
+{"CGAGAG", -200}, 
+{"CGCAAG", -200}, 
+{"CGCGAG", -200}, 
+{"CGGAAG", -200}, 
+{"CGUAAG", -200}, 
+{"CGUGAG", -200}, 
+{"CUACGG", -200}, 
+{"CUCCGG", -200}, 
+{"CUUCGG", -200}, 
+{"CUUUAG", -200}, 
+{"GAUUUC", -200}, 
+{"GAUUUU", -200}, 
+{"GCUUGC", -200}, 
+{"GCUUGU", -200}, 
+{"GGAAAC", -200}, 
+{"GGAAAU", -200}, 
+{"GGAGAC", -200}, 
+{"GGAGAU", -200}, 
+{"GGCAAC", -200}, 
+{"GGCAAU", -200}, 
+{"GGCGAC", -200}, 
+{"GGCGAU", -200}, 
+{"GGGAAC", -200}, 
+{"GGGAAU", -200}, 
+{"GGUAAC", -200}, 
+{"GGUAAU", -200}, 
+{"GGUGAC", -200}, 
+{"GGUGAU", -200}, 
+{"GUACGC", -200}, 
+{"GUACGU", -200}, 
+{"GUCCGC", -200}, 
+{"GUCCGU", -200}, 
+{"GUUCGC", -200}, 
+{"GUUCGU", -200}, 
+{"GUUUAC", -200}, 
+{"GUUUAU", -200}, 
+{"UAUUUA", -200}, 
+{"UAUUUG", -200}, 
+{"UCUUGA", -200}, 
+{"UCUUGG", -200}, 
+{"UGAAAA", -200}, 
+{"UGAAAG", -200}, 
+{"UGAGAA", -200}, 
+{"UGAGAG", -200}, 
+{"UGCAAA", -200}, 
+{"UGCAAG", -200}, 
+{"UGCGAA", -200}, 
+{"UGCGAG", -200}, 
+{"UGGAAA", -200}, 
+{"UGGAAG", -200}, 
+{"UGUAAA", -200}, 
+{"UGUAAG", -200}, 
+{"UGUGAA", -200}, 
+{"UGUGAG", -200}, 
+{"UUACGA", -200}, 
+{"UUACGG", -200}, 
+{"UUCCGA", -200}, 
+{"UUCCGG", -200}, 
+{"UUUCGA", -200}, 
+{"UUUCGG", -200}, 
+{"UUUUAA", -200}, 
+{"UUUUAG", -200}, 
+{nullptr, 0}};
+
+static int thermo_params[] = {
+// >Stacking 5' X1 Y1 3'
+// >         3' X2 Y2 5'
+// >X1X2 = AU CG GC UA GU UG (row headings)
+// >Y1Y2 = AU CG GC UA GU UG (column headings)
+-90, -210, -170, -90, -50, -100, 
+-180, -290, -200, -170, -120, -190, 
+-230, -340, -290, -210, -140, -210, 
+-110, -230, -180, -90, -80, -110, 
+-110, -210, -190, -100, -40, 150, 
+-80, -140, -120, -50, -20, -40, 
+// >Hairpin Loop Energies: size = 1,2,3,..,30
+0, 0, 410, 490, 440, 470, 500, 510, 520, 530, 540, 550, 560, 570, 580, 580, 590, 590, 600, 610, 610, 620, 620, 630, 630, 630, 640, 640, 650, 650, 
+ // >Bulge loop Energies: size = 1,2,3,..,30
+390, 310, 350, 420, 480, 500, 520, 530, 540, 550, 570, 570, 580, 590, 600, 610, 610, 620, 620, 630, 630, 640, 640, 650, 650, 650, 660, 670, 670, 670, 
+ // >Interior Loop Energies: size = 1,2,3,..,30
+0, 410, 510, 490, 530, 570, 590, 600, 610, 630, 640, 640, 650, 660, 670, 680, 680, 690, 690, 700, 710, 710, 710, 720, 720, 730, 730, 740, 740, 740, 
+// >NINIO asymmetry Terms: m1, m2, m3, m4, max
+// >Energy = MAX[ max, asymmetry*m#] where # = MIN(4,L1,L2)
+// >and L1, L2 are lengths of each side of loop, 
+// >and asymmetry = |L1-L2|
+30, 30, 30, 30, 300, 
+// >Mismatch HP:
+// >Columns 5'-AU,CG,GC,UA,GU,UG-3'
+// >rows 5'-AA,AC,AG,AU,CA,..,UU-3'
+-80, -140, -110, -100, -80, -120, 
+-100, -200, -130, -80, -100, -140, 
+-170, -210, -200, -180, -170, -200, 
+-100, -190, -130, -90, -100, -140, 
+-70, -100, -110, -70, -70, -90, 
+-70, -110, -60, -60, -70, -90, 
+-70, -100, -60, -30, -70, -70, 
+-70, -80, -50, -50, -70, -70, 
+-150, -210, -230, -180, -150, -200, 
+-100, -190, -150, -90, -100, -140, 
+-100, -140, -140, -120, -100, -130, 
+-100, -190, -150, -90, -100, -140, 
+-80, -140, -80, -30, -80, -90, 
+-80, -150, -80, -60, -80, -110, 
+-80, -140, -80, -30, -80, -90, 
+-80, -120, -70, -50, -80, -90, 
+// >Mismatch Interior:
+// >Columns 5'-AU,CG,GC,UA,GU,UG-3'
+// >rows 5'-AA,AC,AG,AU,CA,..,UU-3'
+-100, -150, -150, -100, -150, -100, 
+-100, -150, -150, -100, -150, -100, 
+-220, -270, -270, -220, -270, -220, 
+-50, -190, -130, -40, -130, -40, 
+-100, -150, -150, -100, -150, -100, 
+-100, -150, -150, -100, -150, -100, 
+-20, -100, -60, 20, -60, 20,
+ -100, -150, -150, -100, -150, -100, 
+ -220, -270, -270, -220, -270, -220,
+  -50, -190, -150, -40, -150, -40, 
+  -100, -150, -150, -100, -150, -100, 
+  -50, -190, -150, -40, -150, -40, 
+  -30, -140, -80, 20, -80, 20, 
+  -100, -150, -150, -100, -150, -100, 
+  -30, -140, -80, 20, -80, 20, 
+  -200, -250, -250, -200, -250, -200, 
+// >Dangle Energies: 5' X1 Y 3'
+// >                 3' X2 . 5'
+// >Columns: Y = A, C, G, U
+// >Rows = X1X2 = AU,CG,GC,UA,GU,UG
+-80, -50, -80, -60, 
+-170, -80, -170, -120, 
+-110, -40, -130, -60, 
+-70, -10, -70, -10, 
+-80, -50, -80, -60, 
+-120, -50, -120, -70, 
+// >Dangle Energies: 5' X1 . 3'
+// >                 3' X2 Y 5'
+// >Columns: Y = A, C, G, U
+// >Rows = X1X2 = AU,CG,GC,UA,GU,UG
+-30, -10, -20, -20, 
+-20, -30, 0, 0, 
+-50, -30, -20, -10, 
+-30, -30, -40, -20, 
+-20, -20, -20, -20, 
+-20, -20, -20, -20, 
+// >Multiloop terms: ALPHA_1, ALPHA_2, ALPHA_3
+// >ML penalty = ALPHA_1 + s * ALPHA_2 + u *ALPHA_3
+// >s = # stems adjacent to ML, u = unpaired bases in ML
+460, 10, 40, 
+// >AT_PENALTY:
+// >Penalty for non GC pairs that terminate a helix
+0, 
+// >Interior Loops 1x1
+// >CG..AU = 5'- C X A 3'
+// >         3'- G Y U 5'
+// >Rows: X = A C G U (X constant for a row)
+// >Columns: Y = A C G U (Y constant in column)
+// AU..AU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// AU..CG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// AU..GC
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// AU..UA
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// AU..GU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// AU..UG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// CG..AU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// CG..CG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// CG..GC
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// CG..UA
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// CG..GU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// CG..UG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GC..AU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GC..CG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GC..GC
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GC..UA
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GC..GU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GC..UG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UA..AU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UA..CG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UA..GC
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UA..UA
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UA..GU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UA..UG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GU..AU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GU..CG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GU..GC
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GU..UA
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GU..GU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// GU..UG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UG..AU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UG..CG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UG..GC
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UG..UA
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UG..GU
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// UG..UG
+80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 
+// >Interior Loops 2x2
+// >CG.AG..AU = 5'- C A G A -3'
+// >            3'- G Y X U -5'
+// >Rows: X = A C G U (X constant for a row)
+// >Columns: Y = A C G U (Y constant in column)
+// AU.AA..AU
+290, 290, 170, 340, 290, 290, 170, 340, 170, 170, 50, 220, 410, 410, 290, 460, 
+// AU.AC..AU
+290, 290, 170, 340, 290, 290, 170, 340, 350, 350, 230, 400, 290, 290, 170, 340, 
+// AU.AG..AU
+170, 170, 50, 220, 410, 410, 290, 460, 290, 290, 170, 340, 410, 410, 290, 460, 
+// AU.AU..AU
+350, 350, 230, 400, 290, 290, 170, 340, 350, 350, 230, 400, 190, 190, 70, 240, 
+// AU.CA..AU
+290, 290, 370, 290, 290, 290, 370, 290, 170, 170, 250, 170, 410, 410, 490, 410, 
+// AU.CC..AU
+290, 290, 370, 290, 290, 290, 370, 290, 350, 350, 430, 350, 290, 290, 370, 290, 
+// AU.CG..AU
+170, 170, 250, 170, 410, 410, 490, 410, 290, 290, 370, 290, 410, 410, 490, 410, 
+// AU.CU..AU
+350, 350, 430, 350, 290, 290, 370, 290, 350, 350, 430, 350, 190, 190, 270, 190, 
+// AU.GA..AU
+170, 340, 290, 340, 170, 340, 290, 340, 50, 220, 170, 220, 290, 460, 410, 460, 
+// AU.GC..AU
+170, 340, 290, 340, 170, 340, 290, 340, 230, 400, 350, 400, 170, 340, 290, 340, 
+// AU.GG..AU
+50, 220, 170, 220, 290, 460, 410, 460, 170, 340, 290, 340, 290, 460, 410, 460, 
+// AU.GU..AU
+230, 400, 350, 400, 170, 340, 290, 340, 230, 400, 350, 400, 70, 240, 190, 240, 
+// AU.UA..AU
+360, 290, 360, 190, 360, 290, 360, 190, 240, 170, 240, 70, 480, 410, 480, 310, 
+// AU.UC..AU
+360, 290, 360, 190, 360, 290, 360, 190, 420, 350, 420, 250, 360, 290, 360, 190, 
+// AU.UG..AU
+240, 170, 240, 70, 480, 410, 480, 310, 360, 290, 360, 190, 480, 410, 480, 310, 
+// AU.UU..AU
+420, 350, 420, 250, 360, 290, 360, 190, 420, 350, 420, 250, 260, 190, 260, 90, 
+// AU.AA..CG
+240, 240, 120, 290, 240, 240, 120, 290, 120, 120, 0, 170, 310, 310, 190, 360, 
+// AU.AC..CG
+240, 240, 120, 290, 240, 240, 120, 290, 240, 240, 120, 290, 240, 240, 120, 290, 
+// AU.AG..CG
+120, 120, 0, 170, 330, 330, 210, 380, 240, 240, 120, 290, 310, 310, 190, 360, 
+// AU.AU..CG
+260, 260, 140, 310, 240, 240, 120, 290, 240, 240, 120, 290, 140, 140, 20, 190, 
+// AU.CA..CG
+240, 240, 320, 240, 240, 240, 320, 240, 120, 120, 200, 120, 310, 310, 390, 310, 
+// AU.CC..CG
+240, 240, 320, 240, 240, 240, 320, 240, 240, 240, 320, 240, 240, 240, 320, 240, 
+// AU.CG..CG
+120, 120, 200, 120, 330, 330, 410, 330, 240, 240, 320, 240, 310, 310, 390, 310, 
+// AU.CU..CG
+260, 260, 340, 260, 240, 240, 320, 240, 240, 240, 320, 240, 140, 140, 220, 140, 
+// AU.GA..CG
+120, 290, 240, 290, 120, 290, 240, 290, 0, 170, 120, 170, 190, 360, 310, 360, 
+// AU.GC..CG
+120, 290, 240, 290, 120, 290, 240, 290, 120, 290, 240, 290, 120, 290, 240, 290, 
+// AU.GG..CG
+0, 170, 120, 170, 210, 380, 330, 380, 120, 290, 240, 290, 190, 360, 310, 360, 
+// AU.GU..CG
+140, 310, 260, 310, 120, 290, 240, 290, 120, 290, 240, 290, 20, 190, 140, 190, 
+// AU.UA..CG
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 380, 310, 380, 210, 
+// AU.UC..CG
+310, 240, 310, 140, 310, 240, 310, 140, 310, 240, 310, 140, 310, 240, 310, 140, 
+// AU.UG..CG
+190, 120, 190, 20, 400, 330, 400, 230, 310, 240, 310, 140, 380, 310, 380, 210, 
+// AU.UU..CG
+330, 260, 330, 160, 310, 240, 310, 140, 310, 240, 310, 140, 210, 140, 210, 40, 
+// AU.AA..GC
+240, 240, 120, 290, 240, 240, 120, 290, 120, 120, 0, 170, 250, 250, 130, 300, 
+// AU.AC..GC
+240, 240, 120, 290, 240, 240, 120, 290, 200, 200, 80, 250, 240, 240, 120, 290, 
+// AU.AG..GC
+120, 120, 0, 170, 290, 290, 170, 340, 240, 240, 120, 290, 250, 250, 130, 300, 
+// AU.AU..GC
+200, 200, 80, 250, 240, 240, 120, 290, 200, 200, 80, 250, 140, 140, 20, 190, 
+// AU.CA..GC
+240, 240, 320, 240, 240, 240, 320, 240, 120, 120, 200, 120, 250, 250, 330, 250, 
+// AU.CC..GC
+240, 240, 320, 240, 240, 240, 320, 240, 200, 200, 280, 200, 240, 240, 320, 240, 
+// AU.CG..GC
+120, 120, 200, 120, 290, 290, 370, 290, 240, 240, 320, 240, 250, 250, 330, 250, 
+// AU.CU..GC
+200, 200, 280, 200, 240, 240, 320, 240, 200, 200, 280, 200, 140, 140, 220, 140, 
+// AU.GA..GC
+120, 290, 240, 290, 120, 290, 240, 290, 0, 170, 120, 170, 130, 300, 250, 300, 
+// AU.GC..GC
+120, 290, 240, 290, 120, 290, 240, 290, 80, 250, 200, 250, 120, 290, 240, 290, 
+// AU.GG..GC
+0, 170, 120, 170, 170, 340, 290, 340, 120, 290, 240, 290, 130, 300, 250, 300, 
+// AU.GU..GC
+80, 250, 200, 250, 120, 290, 240, 290, 80, 250, 200, 250, 20, 190, 140, 190, 
+// AU.UA..GC
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 320, 250, 320, 150, 
+// AU.UC..GC
+310, 240, 310, 140, 310, 240, 310, 140, 270, 200, 270, 100, 310, 240, 310, 140, 
+// AU.UG..GC
+190, 120, 190, 20, 360, 290, 360, 190, 310, 240, 310, 140, 320, 250, 320, 150, 
+// AU.UU..GC
+270, 200, 270, 100, 310, 240, 310, 140, 270, 200, 270, 100, 210, 140, 210, 40, 
+// AU.AA..UA
+290, 290, 170, 340, 290, 290, 170, 340, 170, 170, 50, 220, 360, 360, 240, 410, 
+// AU.AC..UA
+290, 290, 170, 340, 290, 290, 170, 340, 340, 340, 220, 390, 290, 290, 170, 340, 
+// AU.AG..UA
+170, 170, 50, 220, 370, 370, 250, 420, 290, 290, 170, 340, 360, 360, 240, 410, 
+// AU.AU..UA
+340, 340, 220, 390, 290, 290, 170, 340, 340, 340, 220, 390, 190, 190, 70, 240, 
+// AU.CA..UA
+290, 290, 370, 290, 290, 290, 370, 290, 170, 170, 250, 170, 360, 360, 440, 360, 
+// AU.CC..UA
+290, 290, 370, 290, 290, 290, 370, 290, 340, 340, 420, 340, 290, 290, 370, 290, 
+// AU.CG..UA
+170, 170, 250, 170, 370, 370, 450, 370, 290, 290, 370, 290, 360, 360, 440, 360, 
+// AU.CU..UA
+340, 340, 420, 340, 290, 290, 370, 290, 340, 340, 420, 340, 190, 190, 270, 190, 
+// AU.GA..UA
+170, 340, 290, 340, 170, 340, 290, 340, 50, 220, 170, 220, 240, 410, 360, 410, 
+// AU.GC..UA
+170, 340, 290, 340, 170, 340, 290, 340, 220, 390, 340, 390, 170, 340, 290, 340, 
+// AU.GG..UA
+50, 220, 170, 220, 250, 420, 370, 420, 170, 340, 290, 340, 240, 410, 360, 410, 
+// AU.GU..UA
+220, 390, 340, 390, 170, 340, 290, 340, 220, 390, 340, 390, 70, 240, 190, 240, 
+// AU.UA..UA
+360, 290, 360, 190, 360, 290, 360, 190, 240, 170, 240, 70, 430, 360, 430, 260, 
+// AU.UC..UA
+360, 290, 360, 190, 360, 290, 360, 190, 410, 340, 410, 240, 360, 290, 360, 190, 
+// AU.UG..UA
+240, 170, 240, 70, 440, 370, 440, 270, 360, 290, 360, 190, 430, 360, 430, 260, 
+// AU.UU..UA
+410, 340, 410, 240, 360, 290, 360, 190, 410, 340, 410, 240, 260, 190, 260, 90, 
+// AU.AA..GU
+290, 290, 170, 340, 290, 290, 170, 340, 170, 170, 50, 220, 410, 410, 290, 460, 
+// AU.AC..GU
+290, 290, 170, 340, 290, 290, 170, 340, 350, 350, 230, 400, 290, 290, 170, 340, 
+// AU.AG..GU
+170, 170, 50, 220, 410, 410, 290, 460, 290, 290, 170, 340, 410, 410, 290, 460, 
+// AU.AU..GU
+350, 350, 230, 400, 290, 290, 170, 340, 350, 350, 230, 400, 190, 190, 70, 240, 
+// AU.CA..GU
+290, 290, 370, 290, 290, 290, 370, 290, 170, 170, 250, 170, 410, 410, 490, 410, 
+// AU.CC..GU
+290, 290, 370, 290, 290, 290, 370, 290, 350, 350, 430, 350, 290, 290, 370, 290, 
+// AU.CG..GU
+170, 170, 250, 170, 410, 410, 490, 410, 290, 290, 370, 290, 410, 410, 490, 410, 
+// AU.CU..GU
+350, 350, 430, 350, 290, 290, 370, 290, 350, 350, 430, 350, 190, 190, 270, 190, 
+// AU.GA..GU
+170, 340, 290, 340, 170, 340, 290, 340, 50, 220, 170, 220, 290, 460, 410, 460, 
+// AU.GC..GU
+170, 340, 290, 340, 170, 340, 290, 340, 230, 400, 350, 400, 170, 340, 290, 340, 
+// AU.GG..GU
+50, 220, 170, 220, 290, 460, 410, 460, 170, 340, 290, 340, 290, 460, 410, 460, 
+// AU.GU..GU
+230, 400, 350, 400, 170, 340, 290, 340, 230, 400, 350, 400, 70, 240, 190, 240, 
+// AU.UA..GU
+360, 290, 360, 190, 360, 290, 360, 190, 240, 170, 240, 70, 480, 410, 480, 310, 
+// AU.UC..GU
+360, 290, 360, 190, 360, 290, 360, 190, 420, 350, 420, 250, 360, 290, 360, 190, 
+// AU.UG..GU
+240, 170, 240, 70, 480, 410, 480, 310, 360, 290, 360, 190, 480, 410, 480, 310, 
+// AU.UU..GU
+420, 350, 420, 250, 360, 290, 360, 190, 420, 350, 420, 250, 260, 190, 260, 90, 
+// AU.AA..UG
+240, 240, 120, 290, 240, 240, 120, 290, 120, 120, 0, 170, 310, 310, 190, 360, 
+// AU.AC..UG
+240, 240, 120, 290, 240, 240, 120, 290, 240, 240, 120, 290, 240, 240, 120, 290, 
+// AU.AG..UG
+120, 120, 0, 170, 330, 330, 210, 380, 240, 240, 120, 290, 310, 310, 190, 360, 
+// AU.AU..UG
+260, 260, 140, 310, 240, 240, 120, 290, 240, 240, 120, 290, 140, 140, 20, 190, 
+// AU.CA..UG
+240, 240, 320, 240, 240, 240, 320, 240, 120, 120, 200, 120, 310, 310, 390, 310, 
+// AU.CC..UG
+240, 240, 320, 240, 240, 240, 320, 240, 240, 240, 320, 240, 240, 240, 320, 240, 
+// AU.CG..UG
+120, 120, 200, 120, 330, 330, 410, 330, 240, 240, 320, 240, 310, 310, 390, 310, 
+// AU.CU..UG
+260, 260, 340, 260, 240, 240, 320, 240, 240, 240, 320, 240, 140, 140, 220, 140, 
+// AU.GA..UG
+120, 290, 240, 290, 120, 290, 240, 290, 0, 170, 120, 170, 190, 360, 310, 360, 
+// AU.GC..UG
+120, 290, 240, 290, 120, 290, 240, 290, 120, 290, 240, 290, 120, 290, 240, 290, 
+// AU.GG..UG
+0, 170, 120, 170, 210, 380, 330, 380, 120, 290, 240, 290, 190, 360, 310, 360, 
+// AU.GU..UG
+140, 310, 260, 310, 120, 290, 240, 290, 120, 290, 240, 290, 20, 190, 140, 190, 
+// AU.UA..UG
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 380, 310, 380, 210, 
+// AU.UC..UG
+310, 240, 310, 140, 310, 240, 310, 140, 310, 240, 310, 140, 310, 240, 310, 140, 
+// AU.UG..UG
+190, 120, 190, 20, 400, 330, 400, 230, 310, 240, 310, 140, 380, 310, 380, 210, 
+// AU.UU..UG
+330, 260, 330, 160, 310, 240, 310, 140, 310, 240, 310, 140, 210, 140, 210, 40, 
+// CG.AA..AU
+240, 240, 120, 200, 240, 240, 120, 200, 120, 120, 0, 80, 360, 360, 240, 320, 
+// CG.AC..AU
+240, 240, 120, 200, 240, 240, 120, 200, 300, 300, 180, 260, 240, 240, 120, 200, 
+// CG.AG..AU
+120, 120, 0, 80, 360, 360, 240, 320, 240, 240, 120, 200, 360, 360, 240, 320, 
+// CG.AU..AU
+300, 300, 180, 260, 240, 240, 120, 200, 300, 300, 180, 260, 140, 140, 20, 100, 
+// CG.CA..AU
+240, 240, 290, 240, 240, 240, 290, 240, 120, 120, 170, 120, 360, 360, 410, 360, 
+// CG.CC..AU
+240, 240, 290, 240, 240, 240, 290, 240, 300, 300, 350, 300, 240, 240, 290, 240, 
+// CG.CG..AU
+120, 120, 170, 120, 360, 360, 410, 360, 240, 240, 290, 240, 360, 360, 410, 360, 
+// CG.CU..AU
+300, 300, 350, 300, 240, 240, 290, 240, 300, 300, 350, 300, 140, 140, 190, 140, 
+// CG.GA..AU
+120, 200, 240, 200, 120, 200, 240, 200, 0, 80, 120, 80, 240, 320, 360, 320, 
+// CG.GC..AU
+120, 200, 240, 200, 120, 200, 240, 200, 180, 260, 300, 260, 120, 200, 240, 200, 
+// CG.GG..AU
+0, 80, 120, 80, 240, 320, 360, 320, 120, 200, 240, 200, 240, 320, 360, 320, 
+// CG.GU..AU
+180, 260, 300, 260, 120, 200, 240, 200, 180, 260, 300, 260, 20, 100, 140, 100, 
+// CG.UA..AU
+250, 240, 250, 140, 250, 240, 250, 140, 130, 120, 130, 20, 370, 360, 370, 260, 
+// CG.UC..AU
+250, 240, 250, 140, 250, 240, 250, 140, 310, 300, 310, 200, 250, 240, 250, 140, 
+// CG.UG..AU
+130, 120, 130, 20, 370, 360, 370, 260, 250, 240, 250, 140, 370, 360, 370, 260, 
+// CG.UU..AU
+310, 300, 310, 200, 250, 240, 250, 140, 310, 300, 310, 200, 150, 140, 150, 40, 
+// CG.AA..CG
+190, 190, 70, 150, 190, 190, 70, 150, 70, 70, -50, 30, 260, 260, 140, 220, 
+// CG.AC..CG
+190, 190, 70, 150, 190, 190, 70, 150, 190, 190, 70, 150, 190, 190, 70, 150, 
+// CG.AG..CG
+70, 70, -50, 30, 280, 280, 160, 240, 190, 190, 70, 150, 260, 260, 140, 220, 
+// CG.AU..CG
+210, 210, 90, 170, 190, 190, 70, 150, 190, 190, 70, 150, 90, 90, -30, 50, 
+// CG.CA..CG
+190, 190, 240, 190, 190, 190, 240, 190, 70, 70, 120, 70, 260, 260, 310, 260, 
+// CG.CC..CG
+190, 190, 240, 190, 190, 190, 240, 190, 190, 190, 240, 190, 190, 190, 240, 190, 
+// CG.CG..CG
+70, 70, 120, 70, 280, 280, 330, 280, 190, 190, 240, 190, 260, 260, 310, 260, 
+// CG.CU..CG
+210, 210, 260, 210, 190, 190, 240, 190, 190, 190, 240, 190, 90, 90, 140, 90, 
+// CG.GA..CG
+70, 150, 190, 150, 70, 150, 190, 150, -50, 30, 70, 30, 140, 220, 260, 220, 
+// CG.GC..CG
+70, 150, 190, 150, 70, 150, 190, 150, 70, 150, 190, 150, 70, 150, 190, 150, 
+// CG.GG..CG
+-50, 30, 70, 30, 160, 240, 280, 240, 70, 150, 190, 150, 140, 220, 260, 220, 
+// CG.GU..CG
+90, 170, 210, 170, 70, 150, 190, 150, 70, 150, 190, 150, -30, 50, 90, 50, 
+// CG.UA..CG
+200, 190, 200, 90, 200, 190, 200, 90, 80, 70, 80, -30, 270, 260, 270, 160, 
+// CG.UC..CG
+200, 190, 200, 90, 200, 190, 200, 90, 200, 190, 200, 90, 200, 190, 200, 90, 
+// CG.UG..CG
+80, 70, 80, -30, 290, 280, 290, 180, 200, 190, 200, 90, 270, 260, 270, 160, 
+// CG.UU..CG
+220, 210, 220, 110, 200, 190, 200, 90, 200, 190, 200, 90, 100, 90, 100, -10, 
+// CG.AA..GC
+190, 190, 70, 150, 190, 190, 70, 150, 70, 70, -50, 30, 200, 200, 80, 160, 
+// CG.AC..GC
+190, 190, 70, 150, 190, 190, 70, 150, 150, 150, 30, 110, 190, 190, 70, 150, 
+// CG.AG..GC
+70, 70, -50, 30, 240, 240, 120, 200, 190, 190, 70, 150, 200, 200, 80, 160, 
+// CG.AU..GC
+150, 150, 30, 110, 190, 190, 70, 150, 150, 150, 30, 110, 90, 90, -30, 50, 
+// CG.CA..GC
+190, 190, 240, 190, 190, 190, 240, 190, 70, 70, 120, 70, 200, 200, 250, 200, 
+// CG.CC..GC
+190, 190, 240, 190, 190, 190, 240, 190, 150, 150, 200, 150, 190, 190, 240, 190, 
+// CG.CG..GC
+70, 70, 120, 70, 240, 240, 290, 240, 190, 190, 240, 190, 200, 200, 250, 200, 
+// CG.CU..GC
+150, 150, 200, 150, 190, 190, 240, 190, 150, 150, 200, 150, 90, 90, 140, 90, 
+// CG.GA..GC
+70, 150, 190, 150, 70, 150, 190, 150, -50, 30, 70, 30, 80, 160, 200, 160, 
+// CG.GC..GC
+70, 150, 190, 150, 70, 150, 190, 150, 30, 110, 150, 110, 70, 150, 190, 150, 
+// CG.GG..GC
+-50, 30, 70, 30, 120, 200, 240, 200, 70, 150, 190, 150, 80, 160, 200, 160, 
+// CG.GU..GC
+30, 110, 150, 110, 70, 150, 190, 150, 30, 110, 150, 110, -30, 50, 90, 50, 
+// CG.UA..GC
+200, 190, 200, 90, 200, 190, 200, 90, 80, 70, 80, -30, 210, 200, 210, 100, 
+// CG.UC..GC
+200, 190, 200, 90, 200, 190, 200, 90, 160, 150, 160, 50, 200, 190, 200, 90, 
+// CG.UG..GC
+80, 70, 80, -30, 250, 240, 250, 140, 200, 190, 200, 90, 210, 200, 210, 100, 
+// CG.UU..GC
+160, 150, 160, 50, 200, 190, 200, 90, 160, 150, 160, 50, 100, 90, 100, -10, 
+// CG.AA..UA
+240, 240, 120, 200, 240, 240, 120, 200, 120, 120, 0, 80, 310, 310, 190, 270, 
+// CG.AC..UA
+240, 240, 120, 200, 240, 240, 120, 200, 290, 290, 170, 250, 240, 240, 120, 200, 
+// CG.AG..UA
+120, 120, 0, 80, 320, 320, 200, 280, 240, 240, 120, 200, 310, 310, 190, 270, 
+// CG.AU..UA
+290, 290, 170, 250, 240, 240, 120, 200, 290, 290, 170, 250, 140, 140, 20, 100, 
+// CG.CA..UA
+240, 240, 290, 240, 240, 240, 290, 240, 120, 120, 170, 120, 310, 310, 360, 310, 
+// CG.CC..UA
+240, 240, 290, 240, 240, 240, 290, 240, 290, 290, 340, 290, 240, 240, 290, 240, 
+// CG.CG..UA
+120, 120, 170, 120, 320, 320, 370, 320, 240, 240, 290, 240, 310, 310, 360, 310, 
+// CG.CU..UA
+290, 290, 340, 290, 240, 240, 290, 240, 290, 290, 340, 290, 140, 140, 190, 140, 
+// CG.GA..UA
+120, 200, 240, 200, 120, 200, 240, 200, 0, 80, 120, 80, 190, 270, 310, 270, 
+// CG.GC..UA
+120, 200, 240, 200, 120, 200, 240, 200, 170, 250, 290, 250, 120, 200, 240, 200, 
+// CG.GG..UA
+0, 80, 120, 80, 200, 280, 320, 280, 120, 200, 240, 200, 190, 270, 310, 270, 
+// CG.GU..UA
+170, 250, 290, 250, 120, 200, 240, 200, 170, 250, 290, 250, 20, 100, 140, 100, 
+// CG.UA..UA
+250, 240, 250, 140, 250, 240, 250, 140, 130, 120, 130, 20, 320, 310, 320, 210, 
+// CG.UC..UA
+250, 240, 250, 140, 250, 240, 250, 140, 300, 290, 300, 190, 250, 240, 250, 140, 
+// CG.UG..UA
+130, 120, 130, 20, 330, 320, 330, 220, 250, 240, 250, 140, 320, 310, 320, 210, 
+// CG.UU..UA
+300, 290, 300, 190, 250, 240, 250, 140, 300, 290, 300, 190, 150, 140, 150, 40, 
+// CG.AA..GU
+240, 240, 120, 200, 240, 240, 120, 200, 120, 120, 0, 80, 360, 360, 240, 320, 
+// CG.AC..GU
+240, 240, 120, 200, 240, 240, 120, 200, 300, 300, 180, 260, 240, 240, 120, 200, 
+// CG.AG..GU
+120, 120, 0, 80, 360, 360, 240, 320, 240, 240, 120, 200, 360, 360, 240, 320, 
+// CG.AU..GU
+300, 300, 180, 260, 240, 240, 120, 200, 300, 300, 180, 260, 140, 140, 20, 100, 
+// CG.CA..GU
+240, 240, 290, 240, 240, 240, 290, 240, 120, 120, 170, 120, 360, 360, 410, 360, 
+// CG.CC..GU
+240, 240, 290, 240, 240, 240, 290, 240, 300, 300, 350, 300, 240, 240, 290, 240, 
+// CG.CG..GU
+120, 120, 170, 120, 360, 360, 410, 360, 240, 240, 290, 240, 360, 360, 410, 360, 
+// CG.CU..GU
+300, 300, 350, 300, 240, 240, 290, 240, 300, 300, 350, 300, 140, 140, 190, 140, 
+// CG.GA..GU
+120, 200, 240, 200, 120, 200, 240, 200, 0, 80, 120, 80, 240, 320, 360, 320, 
+// CG.GC..GU
+120, 200, 240, 200, 120, 200, 240, 200, 180, 260, 300, 260, 120, 200, 240, 200, 
+// CG.GG..GU
+0, 80, 120, 80, 240, 320, 360, 320, 120, 200, 240, 200, 240, 320, 360, 320, 
+// CG.GU..GU
+180, 260, 300, 260, 120, 200, 240, 200, 180, 260, 300, 260, 20, 100, 140, 100, 
+// CG.UA..GU
+250, 240, 250, 140, 250, 240, 250, 140, 130, 120, 130, 20, 370, 360, 370, 260, 
+// CG.UC..GU
+250, 240, 250, 140, 250, 240, 250, 140, 310, 300, 310, 200, 250, 240, 250, 140, 
+// CG.UG..GU
+130, 120, 130, 20, 370, 360, 370, 260, 250, 240, 250, 140, 370, 360, 370, 260, 
+// CG.UU..GU
+310, 300, 310, 200, 250, 240, 250, 140, 310, 300, 310, 200, 150, 140, 150, 40, 
+// CG.AA..UG
+190, 190, 70, 150, 190, 190, 70, 150, 70, 70, -50, 30, 260, 260, 140, 220, 
+// CG.AC..UG
+190, 190, 70, 150, 190, 190, 70, 150, 190, 190, 70, 150, 190, 190, 70, 150, 
+// CG.AG..UG
+70, 70, -50, 30, 280, 280, 160, 240, 190, 190, 70, 150, 260, 260, 140, 220, 
+// CG.AU..UG
+210, 210, 90, 170, 190, 190, 70, 150, 190, 190, 70, 150, 90, 90, -30, 50, 
+// CG.CA..UG
+190, 190, 240, 190, 190, 190, 240, 190, 70, 70, 120, 70, 260, 260, 310, 260, 
+// CG.CC..UG
+190, 190, 240, 190, 190, 190, 240, 190, 190, 190, 240, 190, 190, 190, 240, 190, 
+// CG.CG..UG
+70, 70, 120, 70, 280, 280, 330, 280, 190, 190, 240, 190, 260, 260, 310, 260, 
+// CG.CU..UG
+210, 210, 260, 210, 190, 190, 240, 190, 190, 190, 240, 190, 90, 90, 140, 90, 
+// CG.GA..UG
+70, 150, 190, 150, 70, 150, 190, 150, -50, 30, 70, 30, 140, 220, 260, 220, 
+// CG.GC..UG
+70, 150, 190, 150, 70, 150, 190, 150, 70, 150, 190, 150, 70, 150, 190, 150, 
+// CG.GG..UG
+-50, 30, 70, 30, 160, 240, 280, 240, 70, 150, 190, 150, 140, 220, 260, 220, 
+// CG.GU..UG
+90, 170, 210, 170, 70, 150, 190, 150, 70, 150, 190, 150, -30, 50, 90, 50, 
+// CG.UA..UG
+200, 190, 200, 90, 200, 190, 200, 90, 80, 70, 80, -30, 270, 260, 270, 160, 
+// CG.UC..UG
+200, 190, 200, 90, 200, 190, 200, 90, 200, 190, 200, 90, 200, 190, 200, 90, 
+// CG.UG..UG
+80, 70, 80, -30, 290, 280, 290, 180, 200, 190, 200, 90, 270, 260, 270, 160, 
+// CG.UU..UG
+220, 210, 220, 110, 200, 190, 200, 90, 200, 190, 200, 90, 100, 90, 100, -10, 
+// GC.AA..AU
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 360, 360, 240, 380, 
+// GC.AC..AU
+240, 240, 120, 260, 240, 240, 120, 260, 300, 300, 180, 320, 240, 240, 120, 260, 
+// GC.AG..AU
+120, 120, 0, 140, 360, 360, 240, 380, 240, 240, 120, 260, 360, 360, 240, 380, 
+// GC.AU..AU
+300, 300, 180, 320, 240, 240, 120, 260, 300, 300, 180, 320, 140, 140, 20, 160, 
+// GC.CA..AU
+240, 240, 330, 240, 240, 240, 330, 240, 120, 120, 210, 120, 360, 360, 450, 360, 
+// GC.CC..AU
+240, 240, 330, 240, 240, 240, 330, 240, 300, 300, 390, 300, 240, 240, 330, 240, 
+// GC.CG..AU
+120, 120, 210, 120, 360, 360, 450, 360, 240, 240, 330, 240, 360, 360, 450, 360, 
+// GC.CU..AU
+300, 300, 390, 300, 240, 240, 330, 240, 300, 300, 390, 300, 140, 140, 230, 140, 
+// GC.GA..AU
+120, 240, 240, 240, 120, 240, 240, 240, 0, 120, 120, 120, 240, 360, 360, 360, 
+// GC.GC..AU
+120, 240, 240, 240, 120, 240, 240, 240, 180, 300, 300, 300, 120, 240, 240, 240, 
+// GC.GG..AU
+0, 120, 120, 120, 240, 360, 360, 360, 120, 240, 240, 240, 240, 360, 360, 360, 
+// GC.GU..AU
+180, 300, 300, 300, 120, 240, 240, 240, 180, 300, 300, 300, 20, 140, 140, 140, 
+// GC.UA..AU
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 430, 360, 430, 260, 
+// GC.UC..AU
+310, 240, 310, 140, 310, 240, 310, 140, 370, 300, 370, 200, 310, 240, 310, 140, 
+// GC.UG..AU
+190, 120, 190, 20, 430, 360, 430, 260, 310, 240, 310, 140, 430, 360, 430, 260, 
+// GC.UU..AU
+370, 300, 370, 200, 310, 240, 310, 140, 370, 300, 370, 200, 210, 140, 210, 40, 
+// GC.AA..CG
+190, 190, 70, 210, 190, 190, 70, 210, 70, 70, -50, 90, 260, 260, 140, 280, 
+// GC.AC..CG
+190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 
+// GC.AG..CG
+70, 70, -50, 90, 280, 280, 160, 300, 190, 190, 70, 210, 260, 260, 140, 280, 
+// GC.AU..CG
+210, 210, 90, 230, 190, 190, 70, 210, 190, 190, 70, 210, 90, 90, -30, 110, 
+// GC.CA..CG
+190, 190, 280, 190, 190, 190, 280, 190, 70, 70, 160, 70, 260, 260, 350, 260, 
+// GC.CC..CG
+190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 
+// GC.CG..CG
+70, 70, 160, 70, 280, 280, 370, 280, 190, 190, 280, 190, 260, 260, 350, 260, 
+// GC.CU..CG
+210, 210, 300, 210, 190, 190, 280, 190, 190, 190, 280, 190, 90, 90, 180, 90, 
+// GC.GA..CG
+70, 190, 190, 190, 70, 190, 190, 190, -50, 70, 70, 70, 140, 260, 260, 260, 
+// GC.GC..CG
+70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 
+// GC.GG..CG
+-50, 70, 70, 70, 160, 280, 280, 280, 70, 190, 190, 190, 140, 260, 260, 260, 
+// GC.GU..CG
+90, 210, 210, 210, 70, 190, 190, 190, 70, 190, 190, 190, -30, 90, 90, 90, 
+// GC.UA..CG
+260, 190, 260, 90, 260, 190, 260, 90, 140, 70, 140, -30, 330, 260, 330, 160, 
+// GC.UC..CG
+260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 
+// GC.UG..CG
+140, 70, 140, -30, 350, 280, 350, 180, 260, 190, 260, 90, 330, 260, 330, 160, 
+// GC.UU..CG
+280, 210, 280, 110, 260, 190, 260, 90, 260, 190, 260, 90, 160, 90, 160, -10, 
+// GC.AA..GC
+190, 190, 70, 210, 190, 190, 70, 210, 70, 70, -50, 90, 200, 200, 80, 220, 
+// GC.AC..GC
+190, 190, 70, 210, 190, 190, 70, 210, 150, 150, 30, 170, 190, 190, 70, 210, 
+// GC.AG..GC
+70, 70, -50, 90, 240, 240, 120, 260, 190, 190, 70, 210, 200, 200, 80, 220, 
+// GC.AU..GC
+150, 150, 30, 170, 190, 190, 70, 210, 150, 150, 30, 170, 90, 90, -30, 110, 
+// GC.CA..GC
+190, 190, 280, 190, 190, 190, 280, 190, 70, 70, 160, 70, 200, 200, 290, 200, 
+// GC.CC..GC
+190, 190, 280, 190, 190, 190, 280, 190, 150, 150, 240, 150, 190, 190, 280, 190, 
+// GC.CG..GC
+70, 70, 160, 70, 240, 240, 330, 240, 190, 190, 280, 190, 200, 200, 290, 200, 
+// GC.CU..GC
+150, 150, 240, 150, 190, 190, 280, 190, 150, 150, 240, 150, 90, 90, 180, 90, 
+// GC.GA..GC
+70, 190, 190, 190, 70, 190, 190, 190, -50, 70, 70, 70, 80, 200, 200, 200, 
+// GC.GC..GC
+70, 190, 190, 190, 70, 190, 190, 190, 30, 150, 150, 150, 70, 190, 190, 190, 
+// GC.GG..GC
+-50, 70, 70, 70, 120, 240, 240, 240, 70, 190, 190, 190, 80, 200, 200, 200, 
+// GC.GU..GC
+30, 150, 150, 150, 70, 190, 190, 190, 30, 150, 150, 150, -30, 90, 90, 90, 
+// GC.UA..GC
+260, 190, 260, 90, 260, 190, 260, 90, 140, 70, 140, -30, 270, 200, 270, 100, 
+// GC.UC..GC
+260, 190, 260, 90, 260, 190, 260, 90, 220, 150, 220, 50, 260, 190, 260, 90, 
+// GC.UG..GC
+140, 70, 140, -30, 310, 240, 310, 140, 260, 190, 260, 90, 270, 200, 270, 100, 
+// GC.UU..GC
+220, 150, 220, 50, 260, 190, 260, 90, 220, 150, 220, 50, 160, 90, 160, -10, 
+// GC.AA..UA
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 310, 310, 190, 330, 
+// GC.AC..UA
+240, 240, 120, 260, 240, 240, 120, 260, 290, 290, 170, 310, 240, 240, 120, 260, 
+// GC.AG..UA
+120, 120, 0, 140, 320, 320, 200, 340, 240, 240, 120, 260, 310, 310, 190, 330, 
+// GC.AU..UA
+290, 290, 170, 310, 240, 240, 120, 260, 290, 290, 170, 310, 140, 140, 20, 160, 
+// GC.CA..UA
+240, 240, 330, 240, 240, 240, 330, 240, 120, 120, 210, 120, 310, 310, 400, 310, 
+// GC.CC..UA
+240, 240, 330, 240, 240, 240, 330, 240, 290, 290, 380, 290, 240, 240, 330, 240, 
+// GC.CG..UA
+120, 120, 210, 120, 320, 320, 410, 320, 240, 240, 330, 240, 310, 310, 400, 310, 
+// GC.CU..UA
+290, 290, 380, 290, 240, 240, 330, 240, 290, 290, 380, 290, 140, 140, 230, 140, 
+// GC.GA..UA
+120, 240, 240, 240, 120, 240, 240, 240, 0, 120, 120, 120, 190, 310, 310, 310, 
+// GC.GC..UA
+120, 240, 240, 240, 120, 240, 240, 240, 170, 290, 290, 290, 120, 240, 240, 240, 
+// GC.GG..UA
+0, 120, 120, 120, 200, 320, 320, 320, 120, 240, 240, 240, 190, 310, 310, 310, 
+// GC.GU..UA
+170, 290, 290, 290, 120, 240, 240, 240, 170, 290, 290, 290, 20, 140, 140, 140, 
+// GC.UA..UA
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 380, 310, 380, 210, 
+// GC.UC..UA
+310, 240, 310, 140, 310, 240, 310, 140, 360, 290, 360, 190, 310, 240, 310, 140, 
+// GC.UG..UA
+190, 120, 190, 20, 390, 320, 390, 220, 310, 240, 310, 140, 380, 310, 380, 210, 
+// GC.UU..UA
+360, 290, 360, 190, 310, 240, 310, 140, 360, 290, 360, 190, 210, 140, 210, 40, 
+// GC.AA..GU
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 360, 360, 240, 380, 
+// GC.AC..GU
+240, 240, 120, 260, 240, 240, 120, 260, 300, 300, 180, 320, 240, 240, 120, 260, 
+// GC.AG..GU
+120, 120, 0, 140, 360, 360, 240, 380, 240, 240, 120, 260, 360, 360, 240, 380, 
+// GC.AU..GU
+300, 300, 180, 320, 240, 240, 120, 260, 300, 300, 180, 320, 140, 140, 20, 160, 
+// GC.CA..GU
+240, 240, 330, 240, 240, 240, 330, 240, 120, 120, 210, 120, 360, 360, 450, 360, 
+// GC.CC..GU
+240, 240, 330, 240, 240, 240, 330, 240, 300, 300, 390, 300, 240, 240, 330, 240, 
+// GC.CG..GU
+120, 120, 210, 120, 360, 360, 450, 360, 240, 240, 330, 240, 360, 360, 450, 360, 
+// GC.CU..GU
+300, 300, 390, 300, 240, 240, 330, 240, 300, 300, 390, 300, 140, 140, 230, 140, 
+// GC.GA..GU
+120, 240, 240, 240, 120, 240, 240, 240, 0, 120, 120, 120, 240, 360, 360, 360, 
+// GC.GC..GU
+120, 240, 240, 240, 120, 240, 240, 240, 180, 300, 300, 300, 120, 240, 240, 240, 
+// GC.GG..GU
+0, 120, 120, 120, 240, 360, 360, 360, 120, 240, 240, 240, 240, 360, 360, 360, 
+// GC.GU..GU
+180, 300, 300, 300, 120, 240, 240, 240, 180, 300, 300, 300, 20, 140, 140, 140, 
+// GC.UA..GU
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 430, 360, 430, 260, 
+// GC.UC..GU
+310, 240, 310, 140, 310, 240, 310, 140, 370, 300, 370, 200, 310, 240, 310, 140, 
+// GC.UG..GU
+190, 120, 190, 20, 430, 360, 430, 260, 310, 240, 310, 140, 430, 360, 430, 260, 
+// GC.UU..GU
+370, 300, 370, 200, 310, 240, 310, 140, 370, 300, 370, 200, 210, 140, 210, 40, 
+// GC.AA..UG
+190, 190, 70, 210, 190, 190, 70, 210, 70, 70, -50, 90, 260, 260, 140, 280, 
+// GC.AC..UG
+190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 
+// GC.AG..UG
+70, 70, -50, 90, 280, 280, 160, 300, 190, 190, 70, 210, 260, 260, 140, 280, 
+// GC.AU..UG
+210, 210, 90, 230, 190, 190, 70, 210, 190, 190, 70, 210, 90, 90, -30, 110, 
+// GC.CA..UG
+190, 190, 280, 190, 190, 190, 280, 190, 70, 70, 160, 70, 260, 260, 350, 260, 
+// GC.CC..UG
+190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 
+// GC.CG..UG
+70, 70, 160, 70, 280, 280, 370, 280, 190, 190, 280, 190, 260, 260, 350, 260, 
+// GC.CU..UG
+210, 210, 300, 210, 190, 190, 280, 190, 190, 190, 280, 190, 90, 90, 180, 90, 
+// GC.GA..UG
+70, 190, 190, 190, 70, 190, 190, 190, -50, 70, 70, 70, 140, 260, 260, 260, 
+// GC.GC..UG
+70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 
+// GC.GG..UG
+-50, 70, 70, 70, 160, 280, 280, 280, 70, 190, 190, 190, 140, 260, 260, 260, 
+// GC.GU..UG
+90, 210, 210, 210, 70, 190, 190, 190, 70, 190, 190, 190, -30, 90, 90, 90, 
+// GC.UA..UG
+260, 190, 260, 90, 260, 190, 260, 90, 140, 70, 140, -30, 330, 260, 330, 160, 
+// GC.UC..UG
+260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 
+// GC.UG..UG
+140, 70, 140, -30, 350, 280, 350, 180, 260, 190, 260, 90, 330, 260, 330, 160, 
+// GC.UU..UG
+280, 210, 280, 110, 260, 190, 260, 90, 260, 190, 260, 90, 160, 90, 160, -10, 
+// UA.AA..AU
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 410, 410, 290, 470, 
+// UA.AC..AU
+290, 290, 170, 350, 290, 290, 170, 350, 350, 350, 230, 410, 290, 290, 170, 350, 
+// UA.AG..AU
+170, 170, 50, 230, 410, 410, 290, 470, 290, 290, 170, 350, 410, 410, 290, 470, 
+// UA.AU..AU
+350, 350, 230, 410, 290, 290, 170, 350, 350, 350, 230, 410, 190, 190, 70, 250, 
+// UA.CA..AU
+290, 290, 410, 290, 290, 290, 410, 290, 170, 170, 290, 170, 410, 410, 530, 410, 
+// UA.CC..AU
+290, 290, 410, 290, 290, 290, 410, 290, 350, 350, 470, 350, 290, 290, 410, 290, 
+// UA.CG..AU
+170, 170, 290, 170, 410, 410, 530, 410, 290, 290, 410, 290, 410, 410, 530, 410, 
+// UA.CU..AU
+350, 350, 470, 350, 290, 290, 410, 290, 350, 350, 470, 350, 190, 190, 310, 190, 
+// UA.GA..AU
+170, 350, 290, 350, 170, 350, 290, 350, 50, 230, 170, 230, 290, 470, 410, 470, 
+// UA.GC..AU
+170, 350, 290, 350, 170, 350, 290, 350, 230, 410, 350, 410, 170, 350, 290, 350, 
+// UA.GG..AU
+50, 230, 170, 230, 290, 470, 410, 470, 170, 350, 290, 350, 290, 470, 410, 470, 
+// UA.GU..AU
+230, 410, 350, 410, 170, 350, 290, 350, 230, 410, 350, 410, 70, 250, 190, 250, 
+// UA.UA..AU
+410, 290, 410, 190, 410, 290, 410, 190, 290, 170, 290, 70, 530, 410, 530, 310, 
+// UA.UC..AU
+410, 290, 410, 190, 410, 290, 410, 190, 470, 350, 470, 250, 410, 290, 410, 190, 
+// UA.UG..AU
+290, 170, 290, 70, 530, 410, 530, 310, 410, 290, 410, 190, 530, 410, 530, 310, 
+// UA.UU..AU
+470, 350, 470, 250, 410, 290, 410, 190, 470, 350, 470, 250, 310, 190, 310, 90, 
+// UA.AA..CG
+240, 240, 120, 300, 240, 240, 120, 300, 120, 120, 0, 180, 310, 310, 190, 370, 
+// UA.AC..CG
+240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 
+// UA.AG..CG
+120, 120, 0, 180, 330, 330, 210, 390, 240, 240, 120, 300, 310, 310, 190, 370, 
+// UA.AU..CG
+260, 260, 140, 320, 240, 240, 120, 300, 240, 240, 120, 300, 140, 140, 20, 200, 
+// UA.CA..CG
+240, 240, 360, 240, 240, 240, 360, 240, 120, 120, 240, 120, 310, 310, 430, 310, 
+// UA.CC..CG
+240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 
+// UA.CG..CG
+120, 120, 240, 120, 330, 330, 450, 330, 240, 240, 360, 240, 310, 310, 430, 310, 
+// UA.CU..CG
+260, 260, 380, 260, 240, 240, 360, 240, 240, 240, 360, 240, 140, 140, 260, 140, 
+// UA.GA..CG
+120, 300, 240, 300, 120, 300, 240, 300, 0, 180, 120, 180, 190, 370, 310, 370, 
+// UA.GC..CG
+120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 
+// UA.GG..CG
+0, 180, 120, 180, 210, 390, 330, 390, 120, 300, 240, 300, 190, 370, 310, 370, 
+// UA.GU..CG
+140, 320, 260, 320, 120, 300, 240, 300, 120, 300, 240, 300, 20, 200, 140, 200, 
+// UA.UA..CG
+360, 240, 360, 140, 360, 240, 360, 140, 240, 120, 240, 20, 430, 310, 430, 210, 
+// UA.UC..CG
+360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 
+// UA.UG..CG
+240, 120, 240, 20, 450, 330, 450, 230, 360, 240, 360, 140, 430, 310, 430, 210, 
+// UA.UU..CG
+380, 260, 380, 160, 360, 240, 360, 140, 360, 240, 360, 140, 260, 140, 260, 40, 
+// UA.AA..GC
+240, 240, 120, 300, 240, 240, 120, 300, 120, 120, 0, 180, 250, 250, 130, 310, 
+// UA.AC..GC
+240, 240, 120, 300, 240, 240, 120, 300, 200, 200, 80, 260, 240, 240, 120, 300, 
+// UA.AG..GC
+120, 120, 0, 180, 290, 290, 170, 350, 240, 240, 120, 300, 250, 250, 130, 310, 
+// UA.AU..GC
+200, 200, 80, 260, 240, 240, 120, 300, 200, 200, 80, 260, 140, 140, 20, 200, 
+// UA.CA..GC
+240, 240, 360, 240, 240, 240, 360, 240, 120, 120, 240, 120, 250, 250, 370, 250, 
+// UA.CC..GC
+240, 240, 360, 240, 240, 240, 360, 240, 200, 200, 320, 200, 240, 240, 360, 240, 
+// UA.CG..GC
+120, 120, 240, 120, 290, 290, 410, 290, 240, 240, 360, 240, 250, 250, 370, 250, 
+// UA.CU..GC
+200, 200, 320, 200, 240, 240, 360, 240, 200, 200, 320, 200, 140, 140, 260, 140, 
+// UA.GA..GC
+120, 300, 240, 300, 120, 300, 240, 300, 0, 180, 120, 180, 130, 310, 250, 310, 
+// UA.GC..GC
+120, 300, 240, 300, 120, 300, 240, 300, 80, 260, 200, 260, 120, 300, 240, 300, 
+// UA.GG..GC
+0, 180, 120, 180, 170, 350, 290, 350, 120, 300, 240, 300, 130, 310, 250, 310, 
+// UA.GU..GC
+80, 260, 200, 260, 120, 300, 240, 300, 80, 260, 200, 260, 20, 200, 140, 200, 
+// UA.UA..GC
+360, 240, 360, 140, 360, 240, 360, 140, 240, 120, 240, 20, 370, 250, 370, 150, 
+// UA.UC..GC
+360, 240, 360, 140, 360, 240, 360, 140, 320, 200, 320, 100, 360, 240, 360, 140, 
+// UA.UG..GC
+240, 120, 240, 20, 410, 290, 410, 190, 360, 240, 360, 140, 370, 250, 370, 150, 
+// UA.UU..GC
+320, 200, 320, 100, 360, 240, 360, 140, 320, 200, 320, 100, 260, 140, 260, 40, 
+// UA.AA..UA
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 360, 360, 240, 420, 
+// UA.AC..UA
+290, 290, 170, 350, 290, 290, 170, 350, 340, 340, 220, 400, 290, 290, 170, 350, 
+// UA.AG..UA
+170, 170, 50, 230, 370, 370, 250, 430, 290, 290, 170, 350, 360, 360, 240, 420, 
+// UA.AU..UA
+340, 340, 220, 400, 290, 290, 170, 350, 340, 340, 220, 400, 190, 190, 70, 250, 
+// UA.CA..UA
+290, 290, 410, 290, 290, 290, 410, 290, 170, 170, 290, 170, 360, 360, 480, 360, 
+// UA.CC..UA
+290, 290, 410, 290, 290, 290, 410, 290, 340, 340, 460, 340, 290, 290, 410, 290, 
+// UA.CG..UA
+170, 170, 290, 170, 370, 370, 490, 370, 290, 290, 410, 290, 360, 360, 480, 360, 
+// UA.CU..UA
+340, 340, 460, 340, 290, 290, 410, 290, 340, 340, 460, 340, 190, 190, 310, 190, 
+// UA.GA..UA
+170, 350, 290, 350, 170, 350, 290, 350, 50, 230, 170, 230, 240, 420, 360, 420, 
+// UA.GC..UA
+170, 350, 290, 350, 170, 350, 290, 350, 220, 400, 340, 400, 170, 350, 290, 350, 
+// UA.GG..UA
+50, 230, 170, 230, 250, 430, 370, 430, 170, 350, 290, 350, 240, 420, 360, 420, 
+// UA.GU..UA
+220, 400, 340, 400, 170, 350, 290, 350, 220, 400, 340, 400, 70, 250, 190, 250, 
+// UA.UA..UA
+410, 290, 410, 190, 410, 290, 410, 190, 290, 170, 290, 70, 480, 360, 480, 260, 
+// UA.UC..UA
+410, 290, 410, 190, 410, 290, 410, 190, 460, 340, 460, 240, 410, 290, 410, 190, 
+// UA.UG..UA
+290, 170, 290, 70, 490, 370, 490, 270, 410, 290, 410, 190, 480, 360, 480, 260, 
+// UA.UU..UA
+460, 340, 460, 240, 410, 290, 410, 190, 460, 340, 460, 240, 310, 190, 310, 90, 
+// UA.AA..GU
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 410, 410, 290, 470, 
+// UA.AC..GU
+290, 290, 170, 350, 290, 290, 170, 350, 350, 350, 230, 410, 290, 290, 170, 350, 
+// UA.AG..GU
+170, 170, 50, 230, 410, 410, 290, 470, 290, 290, 170, 350, 410, 410, 290, 470, 
+// UA.AU..GU
+350, 350, 230, 410, 290, 290, 170, 350, 350, 350, 230, 410, 190, 190, 70, 250, 
+// UA.CA..GU
+290, 290, 410, 290, 290, 290, 410, 290, 170, 170, 290, 170, 410, 410, 530, 410, 
+// UA.CC..GU
+290, 290, 410, 290, 290, 290, 410, 290, 350, 350, 470, 350, 290, 290, 410, 290, 
+// UA.CG..GU
+170, 170, 290, 170, 410, 410, 530, 410, 290, 290, 410, 290, 410, 410, 530, 410, 
+// UA.CU..GU
+350, 350, 470, 350, 290, 290, 410, 290, 350, 350, 470, 350, 190, 190, 310, 190, 
+// UA.GA..GU
+170, 350, 290, 350, 170, 350, 290, 350, 50, 230, 170, 230, 290, 470, 410, 470, 
+// UA.GC..GU
+170, 350, 290, 350, 170, 350, 290, 350, 230, 410, 350, 410, 170, 350, 290, 350, 
+// UA.GG..GU
+50, 230, 170, 230, 290, 470, 410, 470, 170, 350, 290, 350, 290, 470, 410, 470, 
+// UA.GU..GU
+230, 410, 350, 410, 170, 350, 290, 350, 230, 410, 350, 410, 70, 250, 190, 250, 
+// UA.UA..GU
+410, 290, 410, 190, 410, 290, 410, 190, 290, 170, 290, 70, 530, 410, 530, 310, 
+// UA.UC..GU
+410, 290, 410, 190, 410, 290, 410, 190, 470, 350, 470, 250, 410, 290, 410, 190, 
+// UA.UG..GU
+290, 170, 290, 70, 530, 410, 530, 310, 410, 290, 410, 190, 530, 410, 530, 310, 
+// UA.UU..GU
+470, 350, 470, 250, 410, 290, 410, 190, 470, 350, 470, 250, 310, 190, 310, 90, 
+// UA.AA..UG
+240, 240, 120, 300, 240, 240, 120, 300, 120, 120, 0, 180, 310, 310, 190, 370, 
+// UA.AC..UG
+240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 
+// UA.AG..UG
+120, 120, 0, 180, 330, 330, 210, 390, 240, 240, 120, 300, 310, 310, 190, 370, 
+// UA.AU..UG
+260, 260, 140, 320, 240, 240, 120, 300, 240, 240, 120, 300, 140, 140, 20, 200, 
+// UA.CA..UG
+240, 240, 360, 240, 240, 240, 360, 240, 120, 120, 240, 120, 310, 310, 430, 310, 
+// UA.CC..UG
+240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 
+// UA.CG..UG
+120, 120, 240, 120, 330, 330, 450, 330, 240, 240, 360, 240, 310, 310, 430, 310, 
+// UA.CU..UG
+260, 260, 380, 260, 240, 240, 360, 240, 240, 240, 360, 240, 140, 140, 260, 140, 
+// UA.GA..UG
+120, 300, 240, 300, 120, 300, 240, 300, 0, 180, 120, 180, 190, 370, 310, 370, 
+// UA.GC..UG
+120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 
+// UA.GG..UG
+0, 180, 120, 180, 210, 390, 330, 390, 120, 300, 240, 300, 190, 370, 310, 370, 
+// UA.GU..UG
+140, 320, 260, 320, 120, 300, 240, 300, 120, 300, 240, 300, 20, 200, 140, 200, 
+// UA.UA..UG
+360, 240, 360, 140, 360, 240, 360, 140, 240, 120, 240, 20, 430, 310, 430, 210, 
+// UA.UC..UG
+360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 
+// UA.UG..UG
+240, 120, 240, 20, 450, 330, 450, 230, 360, 240, 360, 140, 430, 310, 430, 210, 
+// UA.UU..UG
+380, 260, 380, 160, 360, 240, 360, 140, 360, 240, 360, 140, 260, 140, 260, 40, 
+// GU.AA..AU
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 360, 360, 240, 380, 
+// GU.AC..AU
+240, 240, 120, 260, 240, 240, 120, 260, 300, 300, 180, 320, 240, 240, 120, 260, 
+// GU.AG..AU
+120, 120, 0, 140, 360, 360, 240, 380, 240, 240, 120, 260, 360, 360, 240, 380, 
+// GU.AU..AU
+300, 300, 180, 320, 240, 240, 120, 260, 300, 300, 180, 320, 140, 140, 20, 160, 
+// GU.CA..AU
+240, 240, 330, 240, 240, 240, 330, 240, 120, 120, 210, 120, 360, 360, 450, 360, 
+// GU.CC..AU
+240, 240, 330, 240, 240, 240, 330, 240, 300, 300, 390, 300, 240, 240, 330, 240, 
+// GU.CG..AU
+120, 120, 210, 120, 360, 360, 450, 360, 240, 240, 330, 240, 360, 360, 450, 360, 
+// GU.CU..AU
+300, 300, 390, 300, 240, 240, 330, 240, 300, 300, 390, 300, 140, 140, 230, 140, 
+// GU.GA..AU
+120, 240, 240, 240, 120, 240, 240, 240, 0, 120, 120, 120, 240, 360, 360, 360, 
+// GU.GC..AU
+120, 240, 240, 240, 120, 240, 240, 240, 180, 300, 300, 300, 120, 240, 240, 240, 
+// GU.GG..AU
+0, 120, 120, 120, 240, 360, 360, 360, 120, 240, 240, 240, 240, 360, 360, 360, 
+// GU.GU..AU
+180, 300, 300, 300, 120, 240, 240, 240, 180, 300, 300, 300, 20, 140, 140, 140, 
+// GU.UA..AU
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 430, 360, 430, 260, 
+// GU.UC..AU
+310, 240, 310, 140, 310, 240, 310, 140, 370, 300, 370, 200, 310, 240, 310, 140, 
+// GU.UG..AU
+190, 120, 190, 20, 430, 360, 430, 260, 310, 240, 310, 140, 430, 360, 430, 260, 
+// GU.UU..AU
+370, 300, 370, 200, 310, 240, 310, 140, 370, 300, 370, 200, 210, 140, 210, 40, 
+// GU.AA..CG
+190, 190, 70, 210, 190, 190, 70, 210, 70, 70, -50, 90, 260, 260, 140, 280, 
+// GU.AC..CG
+190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 
+// GU.AG..CG
+70, 70, -50, 90, 280, 280, 160, 300, 190, 190, 70, 210, 260, 260, 140, 280, 
+// GU.AU..CG
+210, 210, 90, 230, 190, 190, 70, 210, 190, 190, 70, 210, 90, 90, -30, 110, 
+// GU.CA..CG
+190, 190, 280, 190, 190, 190, 280, 190, 70, 70, 160, 70, 260, 260, 350, 260, 
+// GU.CC..CG
+190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 
+// GU.CG..CG
+70, 70, 160, 70, 280, 280, 370, 280, 190, 190, 280, 190, 260, 260, 350, 260, 
+// GU.CU..CG
+210, 210, 300, 210, 190, 190, 280, 190, 190, 190, 280, 190, 90, 90, 180, 90, 
+// GU.GA..CG
+70, 190, 190, 190, 70, 190, 190, 190, -50, 70, 70, 70, 140, 260, 260, 260, 
+// GU.GC..CG
+70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 
+// GU.GG..CG
+-50, 70, 70, 70, 160, 280, 280, 280, 70, 190, 190, 190, 140, 260, 260, 260, 
+// GU.GU..CG
+90, 210, 210, 210, 70, 190, 190, 190, 70, 190, 190, 190, -30, 90, 90, 90, 
+// GU.UA..CG
+260, 190, 260, 90, 260, 190, 260, 90, 140, 70, 140, -30, 330, 260, 330, 160, 
+// GU.UC..CG
+260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 
+// GU.UG..CG
+140, 70, 140, -30, 350, 280, 350, 180, 260, 190, 260, 90, 330, 260, 330, 160, 
+// GU.UU..CG
+280, 210, 280, 110, 260, 190, 260, 90, 260, 190, 260, 90, 160, 90, 160, -10, 
+// GU.AA..GC
+190, 190, 70, 210, 190, 190, 70, 210, 70, 70, -50, 90, 200, 200, 80, 220, 
+// GU.AC..GC
+190, 190, 70, 210, 190, 190, 70, 210, 150, 150, 30, 170, 190, 190, 70, 210, 
+// GU.AG..GC
+70, 70, -50, 90, 240, 240, 120, 260, 190, 190, 70, 210, 200, 200, 80, 220, 
+// GU.AU..GC
+150, 150, 30, 170, 190, 190, 70, 210, 150, 150, 30, 170, 90, 90, -30, 110, 
+// GU.CA..GC
+190, 190, 280, 190, 190, 190, 280, 190, 70, 70, 160, 70, 200, 200, 290, 200, 
+// GU.CC..GC
+190, 190, 280, 190, 190, 190, 280, 190, 150, 150, 240, 150, 190, 190, 280, 190, 
+// GU.CG..GC
+70, 70, 160, 70, 240, 240, 330, 240, 190, 190, 280, 190, 200, 200, 290, 200, 
+// GU.CU..GC
+150, 150, 240, 150, 190, 190, 280, 190, 150, 150, 240, 150, 90, 90, 180, 90, 
+// GU.GA..GC
+70, 190, 190, 190, 70, 190, 190, 190, -50, 70, 70, 70, 80, 200, 200, 200, 
+// GU.GC..GC
+70, 190, 190, 190, 70, 190, 190, 190, 30, 150, 150, 150, 70, 190, 190, 190, 
+// GU.GG..GC
+-50, 70, 70, 70, 120, 240, 240, 240, 70, 190, 190, 190, 80, 200, 200, 200, 
+// GU.GU..GC
+30, 150, 150, 150, 70, 190, 190, 190, 30, 150, 150, 150, -30, 90, 90, 90, 
+// GU.UA..GC
+260, 190, 260, 90, 260, 190, 260, 90, 140, 70, 140, -30, 270, 200, 270, 100, 
+// GU.UC..GC
+260, 190, 260, 90, 260, 190, 260, 90, 220, 150, 220, 50, 260, 190, 260, 90, 
+// GU.UG..GC
+140, 70, 140, -30, 310, 240, 310, 140, 260, 190, 260, 90, 270, 200, 270, 100, 
+// GU.UU..GC
+220, 150, 220, 50, 260, 190, 260, 90, 220, 150, 220, 50, 160, 90, 160, -10, 
+// GU.AA..UA
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 310, 310, 190, 330, 
+// GU.AC..UA
+240, 240, 120, 260, 240, 240, 120, 260, 290, 290, 170, 310, 240, 240, 120, 260, 
+// GU.AG..UA
+120, 120, 0, 140, 320, 320, 200, 340, 240, 240, 120, 260, 310, 310, 190, 330, 
+// GU.AU..UA
+290, 290, 170, 310, 240, 240, 120, 260, 290, 290, 170, 310, 140, 140, 20, 160, 
+// GU.CA..UA
+240, 240, 330, 240, 240, 240, 330, 240, 120, 120, 210, 120, 310, 310, 400, 310, 
+// GU.CC..UA
+240, 240, 330, 240, 240, 240, 330, 240, 290, 290, 380, 290, 240, 240, 330, 240, 
+// GU.CG..UA
+120, 120, 210, 120, 320, 320, 410, 320, 240, 240, 330, 240, 310, 310, 400, 310, 
+// GU.CU..UA
+290, 290, 380, 290, 240, 240, 330, 240, 290, 290, 380, 290, 140, 140, 230, 140, 
+// GU.GA..UA
+120, 240, 240, 240, 120, 240, 240, 240, 0, 120, 120, 120, 190, 310, 310, 310, 
+// GU.GC..UA
+120, 240, 240, 240, 120, 240, 240, 240, 170, 290, 290, 290, 120, 240, 240, 240, 
+// GU.GG..UA
+0, 120, 120, 120, 200, 320, 320, 320, 120, 240, 240, 240, 190, 310, 310, 310, 
+// GU.GU..UA
+170, 290, 290, 290, 120, 240, 240, 240, 170, 290, 290, 290, 20, 140, 140, 140, 
+// GU.UA..UA
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 380, 310, 380, 210, 
+// GU.UC..UA
+310, 240, 310, 140, 310, 240, 310, 140, 360, 290, 360, 190, 310, 240, 310, 140, 
+// GU.UG..UA
+190, 120, 190, 20, 390, 320, 390, 220, 310, 240, 310, 140, 380, 310, 380, 210, 
+// GU.UU..UA
+360, 290, 360, 190, 310, 240, 310, 140, 360, 290, 360, 190, 210, 140, 210, 40, 
+// GU.AA..GU
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 360, 360, 240, 380, 
+// GU.AC..GU
+240, 240, 120, 260, 240, 240, 120, 260, 300, 300, 180, 320, 240, 240, 120, 260, 
+// GU.AG..GU
+120, 120, 0, 140, 360, 360, 240, 380, 240, 240, 120, 260, 360, 360, 240, 380, 
+// GU.AU..GU
+300, 300, 180, 320, 240, 240, 120, 260, 300, 300, 180, 320, 140, 140, 20, 160, 
+// GU.CA..GU
+240, 240, 330, 240, 240, 240, 330, 240, 120, 120, 210, 120, 360, 360, 450, 360, 
+// GU.CC..GU
+240, 240, 330, 240, 240, 240, 330, 240, 300, 300, 390, 300, 240, 240, 330, 240, 
+// GU.CG..GU
+120, 120, 210, 120, 360, 360, 450, 360, 240, 240, 330, 240, 360, 360, 450, 360, 
+// GU.CU..GU
+300, 300, 390, 300, 240, 240, 330, 240, 300, 300, 390, 300, 140, 140, 230, 140, 
+// GU.GA..GU
+120, 240, 240, 240, 120, 240, 240, 240, 0, 120, 120, 120, 240, 360, 360, 360, 
+// GU.GC..GU
+120, 240, 240, 240, 120, 240, 240, 240, 180, 300, 300, 300, 120, 240, 240, 240, 
+// GU.GG..GU
+0, 120, 120, 120, 240, 360, 360, 360, 120, 240, 240, 240, 240, 360, 360, 360, 
+// GU.GU..GU
+180, 300, 300, 300, 120, 240, 240, 240, 180, 300, 300, 300, 20, 140, 140, 140, 
+// GU.UA..GU
+310, 240, 310, 140, 310, 240, 310, 140, 190, 120, 190, 20, 430, 360, 430, 260, 
+// GU.UC..GU
+310, 240, 310, 140, 310, 240, 310, 140, 370, 300, 370, 200, 310, 240, 310, 140, 
+// GU.UG..GU
+190, 120, 190, 20, 430, 360, 430, 260, 310, 240, 310, 140, 430, 360, 430, 260, 
+// GU.UU..GU
+370, 300, 370, 200, 310, 240, 310, 140, 370, 300, 370, 200, 210, 140, 210, 40, 
+// GU.AA..UG
+190, 190, 70, 210, 190, 190, 70, 210, 70, 70, -50, 90, 260, 260, 140, 280, 
+// GU.AC..UG
+190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 190, 190, 70, 210, 
+// GU.AG..UG
+70, 70, -50, 90, 280, 280, 160, 300, 190, 190, 70, 210, 260, 260, 140, 280, 
+// GU.AU..UG
+210, 210, 90, 230, 190, 190, 70, 210, 190, 190, 70, 210, 90, 90, -30, 110, 
+// GU.CA..UG
+190, 190, 280, 190, 190, 190, 280, 190, 70, 70, 160, 70, 260, 260, 350, 260, 
+// GU.CC..UG
+190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 190, 190, 280, 190, 
+// GU.CG..UG
+70, 70, 160, 70, 280, 280, 370, 280, 190, 190, 280, 190, 260, 260, 350, 260, 
+// GU.CU..UG
+210, 210, 300, 210, 190, 190, 280, 190, 190, 190, 280, 190, 90, 90, 180, 90, 
+// GU.GA..UG
+70, 190, 190, 190, 70, 190, 190, 190, -50, 70, 70, 70, 140, 260, 260, 260, 
+// GU.GC..UG
+70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 70, 190, 190, 190, 
+// GU.GG..UG
+-50, 70, 70, 70, 160, 280, 280, 280, 70, 190, 190, 190, 140, 260, 260, 260, 
+// GU.GU..UG
+90, 210, 210, 210, 70, 190, 190, 190, 70, 190, 190, 190, -30, 90, 90, 90, 
+// GU.UA..UG
+260, 190, 260, 90, 260, 190, 260, 90, 140, 70, 140, -30, 330, 260, 330, 160, 
+// GU.UC..UG
+260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 260, 190, 260, 90, 
+// GU.UG..UG
+140, 70, 140, -30, 350, 280, 350, 180, 260, 190, 260, 90, 330, 260, 330, 160, 
+// GU.UU..UG
+280, 210, 280, 110, 260, 190, 260, 90, 260, 190, 260, 90, 160, 90, 160, -10, 
+// UG.AA..AU
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 410, 410, 290, 470, 
+// UG.AC..AU
+290, 290, 170, 350, 290, 290, 170, 350, 350, 350, 230, 410, 290, 290, 170, 350, 
+// UG.AG..AU
+170, 170, 50, 230, 410, 410, 290, 470, 290, 290, 170, 350, 410, 410, 290, 470, 
+// UG.AU..AU
+350, 350, 230, 410, 290, 290, 170, 350, 350, 350, 230, 410, 190, 190, 70, 250, 
+// UG.CA..AU
+290, 290, 410, 290, 290, 290, 410, 290, 170, 170, 290, 170, 410, 410, 530, 410, 
+// UG.CC..AU
+290, 290, 410, 290, 290, 290, 410, 290, 350, 350, 470, 350, 290, 290, 410, 290, 
+// UG.CG..AU
+170, 170, 290, 170, 410, 410, 530, 410, 290, 290, 410, 290, 410, 410, 530, 410, 
+// UG.CU..AU
+350, 350, 470, 350, 290, 290, 410, 290, 350, 350, 470, 350, 190, 190, 310, 190, 
+// UG.GA..AU
+170, 350, 290, 350, 170, 350, 290, 350, 50, 230, 170, 230, 290, 470, 410, 470, 
+// UG.GC..AU
+170, 350, 290, 350, 170, 350, 290, 350, 230, 410, 350, 410, 170, 350, 290, 350, 
+// UG.GG..AU
+50, 230, 170, 230, 290, 470, 410, 470, 170, 350, 290, 350, 290, 470, 410, 470, 
+// UG.GU..AU
+230, 410, 350, 410, 170, 350, 290, 350, 230, 410, 350, 410, 70, 250, 190, 250, 
+// UG.UA..AU
+410, 290, 410, 190, 410, 290, 410, 190, 290, 170, 290, 70, 530, 410, 530, 310, 
+// UG.UC..AU
+410, 290, 410, 190, 410, 290, 410, 190, 470, 350, 470, 250, 410, 290, 410, 190, 
+// UG.UG..AU
+290, 170, 290, 70, 530, 410, 530, 310, 410, 290, 410, 190, 530, 410, 530, 310, 
+// UG.UU..AU
+470, 350, 470, 250, 410, 290, 410, 190, 470, 350, 470, 250, 310, 190, 310, 90, 
+// UG.AA..CG
+240, 240, 120, 300, 240, 240, 120, 300, 120, 120, 0, 180, 310, 310, 190, 370, 
+// UG.AC..CG
+240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 
+// UG.AG..CG
+120, 120, 0, 180, 330, 330, 210, 390, 240, 240, 120, 300, 310, 310, 190, 370, 
+// UG.AU..CG
+260, 260, 140, 320, 240, 240, 120, 300, 240, 240, 120, 300, 140, 140, 20, 200, 
+// UG.CA..CG
+240, 240, 360, 240, 240, 240, 360, 240, 120, 120, 240, 120, 310, 310, 430, 310, 
+// UG.CC..CG
+240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 
+// UG.CG..CG
+120, 120, 240, 120, 330, 330, 450, 330, 240, 240, 360, 240, 310, 310, 430, 310, 
+// UG.CU..CG
+260, 260, 380, 260, 240, 240, 360, 240, 240, 240, 360, 240, 140, 140, 260, 140, 
+// UG.GA..CG
+120, 300, 240, 300, 120, 300, 240, 300, 0, 180, 120, 180, 190, 370, 310, 370, 
+// UG.GC..CG
+120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 
+// UG.GG..CG
+0, 180, 120, 180, 210, 390, 330, 390, 120, 300, 240, 300, 190, 370, 310, 370, 
+// UG.GU..CG
+140, 320, 260, 320, 120, 300, 240, 300, 120, 300, 240, 300, 20, 200, 140, 200, 
+// UG.UA..CG
+360, 240, 360, 140, 360, 240, 360, 140, 240, 120, 240, 20, 430, 310, 430, 210, 
+// UG.UC..CG
+360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 
+// UG.UG..CG
+240, 120, 240, 20, 450, 330, 450, 230, 360, 240, 360, 140, 430, 310, 430, 210, 
+// UG.UU..CG
+380, 260, 380, 160, 360, 240, 360, 140, 360, 240, 360, 140, 260, 140, 260, 40, 
+// UG.AA..GC
+240, 240, 120, 300, 240, 240, 120, 300, 120, 120, 0, 180, 250, 250, 130, 310, 
+// UG.AC..GC
+240, 240, 120, 300, 240, 240, 120, 300, 200, 200, 80, 260, 240, 240, 120, 300, 
+// UG.AG..GC
+120, 120, 0, 180, 290, 290, 170, 350, 240, 240, 120, 300, 250, 250, 130, 310, 
+// UG.AU..GC
+200, 200, 80, 260, 240, 240, 120, 300, 200, 200, 80, 260, 140, 140, 20, 200, 
+// UG.CA..GC
+240, 240, 360, 240, 240, 240, 360, 240, 120, 120, 240, 120, 250, 250, 370, 250, 
+// UG.CC..GC
+240, 240, 360, 240, 240, 240, 360, 240, 200, 200, 320, 200, 240, 240, 360, 240, 
+// UG.CG..GC
+120, 120, 240, 120, 290, 290, 410, 290, 240, 240, 360, 240, 250, 250, 370, 250, 
+// UG.CU..GC
+200, 200, 320, 200, 240, 240, 360, 240, 200, 200, 320, 200, 140, 140, 260, 140, 
+// UG.GA..GC
+120, 300, 240, 300, 120, 300, 240, 300, 0, 180, 120, 180, 130, 310, 250, 310, 
+// UG.GC..GC
+120, 300, 240, 300, 120, 300, 240, 300, 80, 260, 200, 260, 120, 300, 240, 300, 
+// UG.GG..GC
+0, 180, 120, 180, 170, 350, 290, 350, 120, 300, 240, 300, 130, 310, 250, 310, 
+// UG.GU..GC
+80, 260, 200, 260, 120, 300, 240, 300, 80, 260, 200, 260, 20, 200, 140, 200, 
+// UG.UA..GC
+360, 240, 360, 140, 360, 240, 360, 140, 240, 120, 240, 20, 370, 250, 370, 150, 
+// UG.UC..GC
+360, 240, 360, 140, 360, 240, 360, 140, 320, 200, 320, 100, 360, 240, 360, 140, 
+// UG.UG..GC
+240, 120, 240, 20, 410, 290, 410, 190, 360, 240, 360, 140, 370, 250, 370, 150, 
+// UG.UU..GC
+320, 200, 320, 100, 360, 240, 360, 140, 320, 200, 320, 100, 260, 140, 260, 40, 
+// UG.AA..UA
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 360, 360, 240, 420, 
+// UG.AC..UA
+290, 290, 170, 350, 290, 290, 170, 350, 340, 340, 220, 400, 290, 290, 170, 350, 
+// UG.AG..UA
+170, 170, 50, 230, 370, 370, 250, 430, 290, 290, 170, 350, 360, 360, 240, 420, 
+// UG.AU..UA
+340, 340, 220, 400, 290, 290, 170, 350, 340, 340, 220, 400, 190, 190, 70, 250, 
+// UG.CA..UA
+290, 290, 410, 290, 290, 290, 410, 290, 170, 170, 290, 170, 360, 360, 480, 360, 
+// UG.CC..UA
+290, 290, 410, 290, 290, 290, 410, 290, 340, 340, 460, 340, 290, 290, 410, 290, 
+// UG.CG..UA
+170, 170, 290, 170, 370, 370, 490, 370, 290, 290, 410, 290, 360, 360, 480, 360, 
+// UG.CU..UA
+340, 340, 460, 340, 290, 290, 410, 290, 340, 340, 460, 340, 190, 190, 310, 190, 
+// UG.GA..UA
+170, 350, 290, 350, 170, 350, 290, 350, 50, 230, 170, 230, 240, 420, 360, 420, 
+// UG.GC..UA
+170, 350, 290, 350, 170, 350, 290, 350, 220, 400, 340, 400, 170, 350, 290, 350, 
+// UG.GG..UA
+50, 230, 170, 230, 250, 430, 370, 430, 170, 350, 290, 350, 240, 420, 360, 420, 
+// UG.GU..UA
+220, 400, 340, 400, 170, 350, 290, 350, 220, 400, 340, 400, 70, 250, 190, 250, 
+// UG.UA..UA
+410, 290, 410, 190, 410, 290, 410, 190, 290, 170, 290, 70, 480, 360, 480, 260, 
+// UG.UC..UA
+410, 290, 410, 190, 410, 290, 410, 190, 460, 340, 460, 240, 410, 290, 410, 190, 
+// UG.UG..UA
+290, 170, 290, 70, 490, 370, 490, 270, 410, 290, 410, 190, 480, 360, 480, 260, 
+// UG.UU..UA
+460, 340, 460, 240, 410, 290, 410, 190, 460, 340, 460, 240, 310, 190, 310, 90, 
+// UG.AA..GU
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 410, 410, 290, 470, 
+// UG.AC..GU
+290, 290, 170, 350, 290, 290, 170, 350, 350, 350, 230, 410, 290, 290, 170, 350, 
+// UG.AG..GU
+170, 170, 50, 230, 410, 410, 290, 470, 290, 290, 170, 350, 410, 410, 290, 470, 
+// UG.AU..GU
+350, 350, 230, 410, 290, 290, 170, 350, 350, 350, 230, 410, 190, 190, 70, 250, 
+// UG.CA..GU
+290, 290, 410, 290, 290, 290, 410, 290, 170, 170, 290, 170, 410, 410, 530, 410, 
+// UG.CC..GU
+290, 290, 410, 290, 290, 290, 410, 290, 350, 350, 470, 350, 290, 290, 410, 290, 
+// UG.CG..GU
+170, 170, 290, 170, 410, 410, 530, 410, 290, 290, 410, 290, 410, 410, 530, 410, 
+// UG.CU..GU
+350, 350, 470, 350, 290, 290, 410, 290, 350, 350, 470, 350, 190, 190, 310, 190, 
+// UG.GA..GU
+170, 350, 290, 350, 170, 350, 290, 350, 50, 230, 170, 230, 290, 470, 410, 470, 
+// UG.GC..GU
+170, 350, 290, 350, 170, 350, 290, 350, 230, 410, 350, 410, 170, 350, 290, 350, 
+// UG.GG..GU
+50, 230, 170, 230, 290, 470, 410, 470, 170, 350, 290, 350, 290, 470, 410, 470, 
+// UG.GU..GU
+230, 410, 350, 410, 170, 350, 290, 350, 230, 410, 350, 410, 70, 250, 190, 250, 
+// UG.UA..GU
+410, 290, 410, 190, 410, 290, 410, 190, 290, 170, 290, 70, 530, 410, 530, 310, 
+// UG.UC..GU
+410, 290, 410, 190, 410, 290, 410, 190, 470, 350, 470, 250, 410, 290, 410, 190, 
+// UG.UG..GU
+290, 170, 290, 70, 530, 410, 530, 310, 410, 290, 410, 190, 530, 410, 530, 310, 
+// UG.UU..GU
+470, 350, 470, 250, 410, 290, 410, 190, 470, 350, 470, 250, 310, 190, 310, 90, 
+// UG.AA..UG
+240, 240, 120, 300, 240, 240, 120, 300, 120, 120, 0, 180, 310, 310, 190, 370, 
+// UG.AC..UG
+240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 240, 240, 120, 300, 
+// UG.AG..UG
+120, 120, 0, 180, 330, 330, 210, 390, 240, 240, 120, 300, 310, 310, 190, 370, 
+// UG.AU..UG
+260, 260, 140, 320, 240, 240, 120, 300, 240, 240, 120, 300, 140, 140, 20, 200, 
+// UG.CA..UG
+240, 240, 360, 240, 240, 240, 360, 240, 120, 120, 240, 120, 310, 310, 430, 310, 
+// UG.CC..UG
+240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 240, 240, 360, 240, 
+// UG.CG..UG
+120, 120, 240, 120, 330, 330, 450, 330, 240, 240, 360, 240, 310, 310, 430, 310, 
+// UG.CU..UG
+260, 260, 380, 260, 240, 240, 360, 240, 240, 240, 360, 240, 140, 140, 260, 140, 
+// UG.GA..UG
+120, 300, 240, 300, 120, 300, 240, 300, 0, 180, 120, 180, 190, 370, 310, 370, 
+// UG.GC..UG
+120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 120, 300, 240, 300, 
+// UG.GG..UG
+0, 180, 120, 180, 210, 390, 330, 390, 120, 300, 240, 300, 190, 370, 310, 370, 
+// UG.GU..UG
+140, 320, 260, 320, 120, 300, 240, 300, 120, 300, 240, 300, 20, 200, 140, 200, 
+// UG.UA..UG
+360, 240, 360, 140, 360, 240, 360, 140, 240, 120, 240, 20, 430, 310, 430, 210, 
+// UG.UC..UG
+360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 360, 240, 360, 140, 
+// UG.UG..UG
+240, 120, 240, 20, 450, 330, 450, 230, 360, 240, 360, 140, 430, 310, 430, 210, 
+// UG.UU..UG
+380, 260, 380, 160, 360, 240, 360, 140, 360, 240, 360, 140, 260, 140, 260, 40, 
+// >Interior Loops 1x2
+// >CG.A..AU = 5'- C A   A -3'
+// >           3'- G Y X U -5'
+// >Rows: X = A C G U (X constant for a row)
+// >Columns: Y = A C G U (Y constant in column)
+// AU.A..AU
+340, 340, 220, 390, 340, 340, 220, 390, 220, 220, 100, 270, 460, 460, 340, 510, 
+// AU.C..AU
+340, 340, 420, 340, 340, 340, 420, 340, 400, 400, 480, 400, 340, 340, 420, 340, 
+// AU.G..AU
+100, 270, 220, 270, 340, 510, 460, 510, 220, 390, 340, 390, 340, 510, 460, 510, 
+// AU.U..AU
+470, 400, 470, 300, 410, 340, 410, 240, 470, 400, 470, 300, 310, 240, 310, 140, 
+// AU.A..CG
+290, 290, 170, 340, 290, 290, 170, 340, 170, 170, 50, 220, 360, 360, 240, 410, 
+// AU.C..CG
+290, 290, 370, 290, 290, 290, 370, 290, 290, 290, 370, 290, 290, 290, 370, 290, 
+// AU.G..CG
+50, 220, 170, 220, 260, 430, 380, 430, 170, 340, 290, 340, 240, 410, 360, 410, 
+// AU.U..CG
+380, 310, 380, 210, 360, 290, 360, 190, 360, 290, 360, 190, 260, 190, 260, 90, 
+// AU.A..GC
+290, 290, 170, 340, 290, 290, 170, 340, 170, 170, 50, 220, 300, 300, 180, 350, 
+// AU.C..GC
+290, 290, 370, 290, 290, 290, 370, 290, 250, 250, 330, 250, 290, 290, 370, 290, 
+// AU.G..GC
+50, 220, 170, 220, 220, 390, 340, 390, 170, 340, 290, 340, 180, 350, 300, 350, 
+// AU.U..GC
+320, 250, 320, 150, 360, 290, 360, 190, 320, 250, 320, 150, 260, 190, 260, 90, 
+// AU.A..UA
+340, 340, 220, 390, 340, 340, 220, 390, 220, 220, 100, 270, 410, 410, 290, 460, 
+// AU.C..UA
+340, 340, 420, 340, 340, 340, 420, 340, 390, 390, 470, 390, 340, 340, 420, 340, 
+// AU.G..UA
+100, 270, 220, 270, 300, 470, 420, 470, 220, 390, 340, 390, 290, 460, 410, 460, 
+// AU.U..UA
+460, 390, 460, 290, 410, 340, 410, 240, 460, 390, 460, 290, 310, 240, 310, 140, 
+// AU.A..GU
+340, 340, 220, 390, 340, 340, 220, 390, 220, 220, 100, 270, 460, 460, 340, 510, 
+// AU.C..GU
+340, 340, 420, 340, 340, 340, 420, 340, 400, 400, 480, 400, 340, 340, 420, 340, 
+// AU.G..GU
+100, 270, 220, 270, 340, 510, 460, 510, 220, 390, 340, 390, 340, 510, 460, 510, 
+// AU.U..GU
+470, 400, 470, 300, 410, 340, 410, 240, 470, 400, 470, 300, 310, 240, 310, 140, 
+// AU.A..UG
+290, 290, 170, 340, 290, 290, 170, 340, 170, 170, 50, 220, 360, 360, 240, 410, 
+// AU.C..UG
+290, 290, 370, 290, 290, 290, 370, 290, 290, 290, 370, 290, 290, 290, 370, 290, 
+// AU.G..UG
+50, 220, 170, 220, 260, 430, 380, 430, 170, 340, 290, 340, 240, 410, 360, 410, 
+// AU.U..UG
+380, 310, 380, 210, 360, 290, 360, 190, 360, 290, 360, 190, 260, 190, 260, 90, 
+// CG.A..AU
+290, 290, 170, 250, 290, 290, 170, 250, 170, 170, 50, 130, 410, 410, 290, 370, 
+// CG.C..AU
+290, 290, 340, 290, 290, 290, 340, 290, 350, 350, 400, 350, 290, 290, 340, 290, 
+// CG.G..AU
+50, 130, 170, 130, 290, 370, 410, 370, 170, 250, 290, 250, 290, 370, 410, 370, 
+// CG.U..AU
+360, 350, 360, 250, 300, 290, 300, 190, 360, 350, 360, 250, 200, 190, 200, 90, 
+// CG.A..CG
+240, 240, 120, 200, 240, 240, 120, 200, 120, 120, 0, 80, 310, 310, 190, 270, 
+// CG.C..CG
+240, 240, 290, 240, 240, 240, 290, 240, 240, 240, 290, 240, 240, 240, 290, 240, 
+// CG.G..CG
+0, 80, 120, 80, 210, 290, 330, 290, 120, 200, 240, 200, 190, 270, 310, 270, 
+// CG.U..CG
+270, 260, 270, 160, 250, 240, 250, 140, 250, 240, 250, 140, 150, 140, 150, 40, 
+// CG.A..GC
+240, 240, 120, 200, 240, 240, 120, 200, 120, 120, 0, 80, 250, 250, 130, 210, 
+// CG.C..GC
+240, 240, 290, 240, 240, 240, 290, 240, 200, 200, 250, 200, 240, 240, 290, 240, 
+// CG.G..GC
+0, 80, 120, 80, 170, 250, 290, 250, 120, 200, 240, 200, 130, 210, 250, 210, 
+// CG.U..GC
+210, 200, 210, 100, 250, 240, 250, 140, 210, 200, 210, 100, 150, 140, 150, 40, 
+// CG.A..UA
+290, 290, 170, 250, 290, 290, 170, 250, 170, 170, 50, 130, 360, 360, 240, 320, 
+// CG.C..UA
+290, 290, 340, 290, 290, 290, 340, 290, 340, 340, 390, 340, 290, 290, 340, 290, 
+// CG.G..UA
+50, 130, 170, 130, 250, 330, 370, 330, 170, 250, 290, 250, 240, 320, 360, 320, 
+// CG.U..UA
+350, 340, 350, 240, 300, 290, 300, 190, 350, 340, 350, 240, 200, 190, 200, 90, 
+// CG.A..GU
+290, 290, 170, 250, 290, 290, 170, 250, 170, 170, 50, 130, 410, 410, 290, 370, 
+// CG.C..GU
+290, 290, 340, 290, 290, 290, 340, 290, 350, 350, 400, 350, 290, 290, 340, 290, 
+// CG.G..GU
+50, 130, 170, 130, 290, 370, 410, 370, 170, 250, 290, 250, 290, 370, 410, 370, 
+// CG.U..GU
+360, 350, 360, 250, 300, 290, 300, 190, 360, 350, 360, 250, 200, 190, 200, 90, 
+// CG.A..UG
+240, 240, 120, 200, 240, 240, 120, 200, 120, 120, 0, 80, 310, 310, 190, 270, 
+// CG.C..UG
+240, 240, 290, 240, 240, 240, 290, 240, 240, 240, 290, 240, 240, 240, 290, 240, 
+// CG.G..UG
+0, 80, 120, 80, 210, 290, 330, 290, 120, 200, 240, 200, 190, 270, 310, 270, 
+// CG.U..UG
+270, 260, 270, 160, 250, 240, 250, 140, 250, 240, 250, 140, 150, 140, 150, 40, 
+// GC.A..AU
+290, 290, 170, 310, 290, 290, 170, 310, 170, 170, 50, 190, 410, 410, 290, 430, 
+// GC.C..AU
+290, 290, 380, 290, 290, 290, 380, 290, 350, 350, 440, 350, 290, 290, 380, 290, 
+// GC.G..AU
+50, 170, 170, 170, 290, 410, 410, 410, 170, 290, 290, 290, 290, 410, 410, 410, 
+// GC.U..AU
+420, 350, 420, 250, 360, 290, 360, 190, 420, 350, 420, 250, 260, 190, 260, 90, 
+// GC.A..CG
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 310, 310, 190, 330, 
+// GC.C..CG
+240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 
+// GC.G..CG
+0, 120, 120, 120, 210, 330, 330, 330, 120, 240, 240, 240, 190, 310, 310, 310, 
+// GC.U..CG
+330, 260, 330, 160, 310, 240, 310, 140, 310, 240, 310, 140, 210, 140, 210, 40, 
+// GC.A..GC
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 250, 250, 130, 270, 
+// GC.C..GC
+240, 240, 330, 240, 240, 240, 330, 240, 200, 200, 290, 200, 240, 240, 330, 240, 
+// GC.G..GC
+0, 120, 120, 120, 170, 290, 290, 290, 120, 240, 240, 240, 130, 250, 250, 250, 
+// GC.U..GC
+270, 200, 270, 100, 310, 240, 310, 140, 270, 200, 270, 100, 210, 140, 210, 40, 
+// GC.A..UA
+290, 290, 170, 310, 290, 290, 170, 310, 170, 170, 50, 190, 360, 360, 240, 380, 
+// GC.C..UA
+290, 290, 380, 290, 290, 290, 380, 290, 340, 340, 430, 340, 290, 290, 380, 290, 
+// GC.G..UA
+50, 170, 170, 170, 250, 370, 370, 370, 170, 290, 290, 290, 240, 360, 360, 360, 
+// GC.U..UA
+410, 340, 410, 240, 360, 290, 360, 190, 410, 340, 410, 240, 260, 190, 260, 90, 
+// GC.A..GU
+290, 290, 170, 310, 290, 290, 170, 310, 170, 170, 50, 190, 410, 410, 290, 430, 
+// GC.C..GU
+290, 290, 380, 290, 290, 290, 380, 290, 350, 350, 440, 350, 290, 290, 380, 290, 
+// GC.G..GU
+50, 170, 170, 170, 290, 410, 410, 410, 170, 290, 290, 290, 290, 410, 410, 410, 
+// GC.U..GU
+420, 350, 420, 250, 360, 290, 360, 190, 420, 350, 420, 250, 260, 190, 260, 90, 
+// GC.A..UG
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 310, 310, 190, 330, 
+// GC.C..UG
+240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 
+// GC.G..UG
+0, 120, 120, 120, 210, 330, 330, 330, 120, 240, 240, 240, 190, 310, 310, 310, 
+// GC.U..UG
+330, 260, 330, 160, 310, 240, 310, 140, 310, 240, 310, 140, 210, 140, 210, 40, 
+// UA.A..AU
+340, 340, 220, 400, 340, 340, 220, 400, 220, 220, 100, 280, 460, 460, 340, 520, 
+// UA.C..AU
+340, 340, 460, 340, 340, 340, 460, 340, 400, 400, 520, 400, 340, 340, 460, 340, 
+// UA.G..AU
+100, 280, 220, 280, 340, 520, 460, 520, 220, 400, 340, 400, 340, 520, 460, 520, 
+// UA.U..AU
+520, 400, 520, 300, 460, 340, 460, 240, 520, 400, 520, 300, 360, 240, 360, 140, 
+// UA.A..CG
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 360, 360, 240, 420, 
+// UA.C..CG
+290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 
+// UA.G..CG
+50, 230, 170, 230, 260, 440, 380, 440, 170, 350, 290, 350, 240, 420, 360, 420, 
+// UA.U..CG
+430, 310, 430, 210, 410, 290, 410, 190, 410, 290, 410, 190, 310, 190, 310, 90, 
+// UA.A..GC
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 300, 300, 180, 360, 
+// UA.C..GC
+290, 290, 410, 290, 290, 290, 410, 290, 250, 250, 370, 250, 290, 290, 410, 290, 
+// UA.G..GC
+50, 230, 170, 230, 220, 400, 340, 400, 170, 350, 290, 350, 180, 360, 300, 360, 
+// UA.U..GC
+370, 250, 370, 150, 410, 290, 410, 190, 370, 250, 370, 150, 310, 190, 310, 90, 
+// UA.A..UA
+340, 340, 220, 400, 340, 340, 220, 400, 220, 220, 100, 280, 410, 410, 290, 470, 
+// UA.C..UA
+340, 340, 460, 340, 340, 340, 460, 340, 390, 390, 510, 390, 340, 340, 460, 340, 
+// UA.G..UA
+100, 280, 220, 280, 300, 480, 420, 480, 220, 400, 340, 400, 290, 470, 410, 470, 
+// UA.U..UA
+510, 390, 510, 290, 460, 340, 460, 240, 510, 390, 510, 290, 360, 240, 360, 140, 
+// UA.A..GU
+340, 340, 220, 400, 340, 340, 220, 400, 220, 220, 100, 280, 460, 460, 340, 520, 
+// UA.C..GU
+340, 340, 460, 340, 340, 340, 460, 340, 400, 400, 520, 400, 340, 340, 460, 340, 
+// UA.G..GU
+100, 280, 220, 280, 340, 520, 460, 520, 220, 400, 340, 400, 340, 520, 460, 520, 
+// UA.U..GU
+520, 400, 520, 300, 460, 340, 460, 240, 520, 400, 520, 300, 360, 240, 360, 140, 
+// UA.A..UG
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 360, 360, 240, 420, 
+// UA.C..UG
+290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 
+// UA.G..UG
+50, 230, 170, 230, 260, 440, 380, 440, 170, 350, 290, 350, 240, 420, 360, 420, 
+// UA.U..UG
+430, 310, 430, 210, 410, 290, 410, 190, 410, 290, 410, 190, 310, 190, 310, 90, 
+// GU.A..AU
+290, 290, 170, 310, 290, 290, 170, 310, 170, 170, 50, 190, 410, 410, 290, 430, 
+// GU.C..AU
+290, 290, 380, 290, 290, 290, 380, 290, 350, 350, 440, 350, 290, 290, 380, 290, 
+// GU.G..AU
+50, 170, 170, 170, 290, 410, 410, 410, 170, 290, 290, 290, 290, 410, 410, 410, 
+// GU.U..AU
+420, 350, 420, 250, 360, 290, 360, 190, 420, 350, 420, 250, 260, 190, 260, 90, 
+// GU.A..CG
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 310, 310, 190, 330, 
+// GU.C..CG
+240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 
+// GU.G..CG
+0, 120, 120, 120, 210, 330, 330, 330, 120, 240, 240, 240, 190, 310, 310, 310, 
+// GU.U..CG
+330, 260, 330, 160, 310, 240, 310, 140, 310, 240, 310, 140, 210, 140, 210, 40, 
+// GU.A..GC
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 250, 250, 130, 270, 
+// GU.C..GC
+240, 240, 330, 240, 240, 240, 330, 240, 200, 200, 290, 200, 240, 240, 330, 240, 
+// GU.G..GC
+0, 120, 120, 120, 170, 290, 290, 290, 120, 240, 240, 240, 130, 250, 250, 250, 
+// GU.U..GC
+270, 200, 270, 100, 310, 240, 310, 140, 270, 200, 270, 100, 210, 140, 210, 40, 
+// GU.A..UA
+290, 290, 170, 310, 290, 290, 170, 310, 170, 170, 50, 190, 360, 360, 240, 380, 
+// GU.C..UA
+290, 290, 380, 290, 290, 290, 380, 290, 340, 340, 430, 340, 290, 290, 380, 290, 
+// GU.G..UA
+50, 170, 170, 170, 250, 370, 370, 370, 170, 290, 290, 290, 240, 360, 360, 360, 
+// GU.U..UA
+410, 340, 410, 240, 360, 290, 360, 190, 410, 340, 410, 240, 260, 190, 260, 90, 
+// GU.A..GU
+290, 290, 170, 310, 290, 290, 170, 310, 170, 170, 50, 190, 410, 410, 290, 430, 
+// GU.C..GU
+290, 290, 380, 290, 290, 290, 380, 290, 350, 350, 440, 350, 290, 290, 380, 290, 
+// GU.G..GU
+50, 170, 170, 170, 290, 410, 410, 410, 170, 290, 290, 290, 290, 410, 410, 410, 
+// GU.U..GU
+420, 350, 420, 250, 360, 290, 360, 190, 420, 350, 420, 250, 260, 190, 260, 90, 
+// GU.A..UG
+240, 240, 120, 260, 240, 240, 120, 260, 120, 120, 0, 140, 310, 310, 190, 330, 
+// GU.C..UG
+240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 240, 240, 330, 240, 
+// GU.G..UG
+0, 120, 120, 120, 210, 330, 330, 330, 120, 240, 240, 240, 190, 310, 310, 310, 
+// GU.U..UG
+330, 260, 330, 160, 310, 240, 310, 140, 310, 240, 310, 140, 210, 140, 210, 40, 
+// UG.A..AU
+340, 340, 220, 400, 340, 340, 220, 400, 220, 220, 100, 280, 460, 460, 340, 520, 
+// UG.C..AU
+340, 340, 460, 340, 340, 340, 460, 340, 400, 400, 520, 400, 340, 340, 460, 340, 
+// UG.G..AU
+100, 280, 220, 280, 340, 520, 460, 520, 220, 400, 340, 400, 340, 520, 460, 520, 
+// UG.U..AU
+520, 400, 520, 300, 460, 340, 460, 240, 520, 400, 520, 300, 360, 240, 360, 140, 
+// UG.A..CG
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 360, 360, 240, 420, 
+// UG.C..CG
+290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 
+// UG.G..CG
+50, 230, 170, 230, 260, 440, 380, 440, 170, 350, 290, 350, 240, 420, 360, 420, 
+// UG.U..CG
+430, 310, 430, 210, 410, 290, 410, 190, 410, 290, 410, 190, 310, 190, 310, 90, 
+// UG.A..GC
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 300, 300, 180, 360, 
+// UG.C..GC
+290, 290, 410, 290, 290, 290, 410, 290, 250, 250, 370, 250, 290, 290, 410, 290, 
+// UG.G..GC
+50, 230, 170, 230, 220, 400, 340, 400, 170, 350, 290, 350, 180, 360, 300, 360, 
+// UG.U..GC
+370, 250, 370, 150, 410, 290, 410, 190, 370, 250, 370, 150, 310, 190, 310, 90, 
+// UG.A..UA
+340, 340, 220, 400, 340, 340, 220, 400, 220, 220, 100, 280, 410, 410, 290, 470, 
+// UG.C..UA
+340, 340, 460, 340, 340, 340, 460, 340, 390, 390, 510, 390, 340, 340, 460, 340, 
+// UG.G..UA
+100, 280, 220, 280, 300, 480, 420, 480, 220, 400, 340, 400, 290, 470, 410, 470, 
+// UG.U..UA
+510, 390, 510, 290, 460, 340, 460, 240, 510, 390, 510, 290, 360, 240, 360, 140, 
+// UG.A..GU
+340, 340, 220, 400, 340, 340, 220, 400, 220, 220, 100, 280, 460, 460, 340, 520, 
+// UG.C..GU
+340, 340, 460, 340, 340, 340, 460, 340, 400, 400, 520, 400, 340, 340, 460, 340, 
+// UG.G..GU
+100, 280, 220, 280, 340, 520, 460, 520, 220, 400, 340, 400, 340, 520, 460, 520, 
+// UG.U..GU
+520, 400, 520, 300, 460, 340, 460, 240, 520, 400, 520, 300, 360, 240, 360, 140, 
+// UG.A..UG
+290, 290, 170, 350, 290, 290, 170, 350, 170, 170, 50, 230, 360, 360, 240, 420, 
+// UG.C..UG
+290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 290, 290, 410, 290, 
+// UG.G..UG
+50, 230, 170, 230, 260, 440, 380, 440, 170, 350, 290, 350, 240, 420, 360, 420, 
+// UG.U..UG
+430, 310, 430, 210, 410, 290, 410, 190, 410, 290, 410, 190, 310, 190, 310, 90, 
+// >POLYC - Penalty for poly C hairpins.
+// >First number is penalty for polyC triloop
+// >Second number is "slope", i.e. penalty per C in a non triloop
+// >Third number is "intercept", i.e. constant penalty for non triloops
+0, 0, 0, 
+// >BETA - Pseudoknot energy parameters.  B1 B2 B3 B1M B1P
+// >B1 = Constant penalty for "open" pseudoknot
+// >B2 = penalty per pair in pseudoknot
+// >B3 = penalty per base in pseudoknot
+// >B1M = constant penalty for pseudoknot in a "closed" loop
+// >B1P = constant penalty for pseudoknot in a pseudoknot.
+960, 10, 10, 1500, 1500, 
+// >BIMOLECULAR //TINOCO, 277
+409 };

+
+@article{djelloul_automated_2008,
+	title = {Automated motif extraction and classification in {RNA} tertiary structures},
+	volume = {14},
+	issn = {1355-8382, 1469-9001},
+	url = {http://rnajournal.cshlp.org/content/14/12/2489},
+	doi = {10.1261/rna.1061108},
+	abstract = {We used a novel graph-based approach to extract RNA tertiary motifs. We cataloged them all and clustered them using an innovative graph similarity measure. We applied our method to three widely studied structures: Haloarcula marismortui 50S (H.m 50S), Escherichia coli 50S (E. coli 50S), and Thermus thermophilus 16S (T.th 16S) RNAs. We identified 10 known motifs without any prior knowledge of their shapes or positions. We additionally identified four putative new motifs.},
+	language = {en},
+	number = {12},
+	urldate = {2018-10-04},
+	journal = {RNA},
+	author = {Djelloul, Mahassine and Denise, Alain},
+	month = jan,
+	year = {2008},
+	pmid = {18957493},
+	keywords = {clustering, graph similarity, RNA tertiary structure},
+	pages = {2489--2497},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/6PDZZRI6/Djelloul et Denise - 2008 - Automated motif extraction and classification in R.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/28T5ICXG/2489.html:text/html}
+}
+
+@article{roll_jar3d_2016,
+	title = {{JAR}3D {Webserver}: {Scoring} and aligning {RNA} loop sequences to known 3D motifs},
+	volume = {44},
+	issn = {0305-1048},
+	shorttitle = {{JAR}3D {Webserver}},
+	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4987954/},
+	doi = {10.1093/nar/gkw453},
+	abstract = {Many non-coding RNAs have been identified and may function by forming 2D and 3D structures. RNA hairpin and internal loops are often represented as unstructured on secondary structure diagrams, but RNA 3D structures show that most such loops are structured by non-Watson–Crick basepairs and base stacking. Moreover, different RNA sequences can form the same RNA 3D motif. JAR3D finds possible 3D geometries for hairpin and internal loops by matching loop sequences to motif groups from the RNA 3D Motif Atlas, by exact sequence match when possible, and by probabilistic scoring and edit distance for novel sequences. The scoring gauges the ability of the sequences to form the same pattern of interactions observed in 3D structures of the motif. The JAR3D webserver at http://rna.bgsu.edu/jar3d/ takes one or many sequences of a single loop as input, or else one or many sequences of longer RNAs with multiple loops. Each sequence is scored against all current motif groups. The output shows the ten best-matching motif groups. Users can align input sequences to each of the motif groups found by JAR3D. JAR3D will be updated with every release of the RNA 3D Motif Atlas, and so its performance is expected to improve over time.},
+	number = {Web Server issue},
+	urldate = {2018-10-04},
+	journal = {Nucleic Acids Research},
+	author = {Roll, James and Zirbel, Craig L. and Sweeney, Blake and Petrov, Anton I. and Leontis, Neocles},
+	month = jul,
+	year = {2016},
+	pmid = {27235417},
+	pmcid = {PMC4987954},
+	pages = {W320--W327},
+	file = {PubMed Central Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/KWD59J5I/Roll et al. - 2016 - JAR3D Webserver Scoring and aligning RNA loop seq.pdf:application/pdf}
+}
+
+@article{zhong_rnamotifscan:_2010,
+	title = {{RNAMotifScan}: automatic identification of {RNA} structural motifs using secondary structural alignment},
+	volume = {38},
+	issn = {0305-1048},
+	shorttitle = {{RNAMotifScan}},
+	url = {https://academic.oup.com/nar/article/38/18/e176/1069222},
+	doi = {10.1093/nar/gkq672},
+	abstract = {Abstract.  Recent studies have shown that RNA structural motifs play essential roles in RNA folding and interaction with other molecules. Computational identifi},
+	language = {en},
+	number = {18},
+	urldate = {2018-10-04},
+	journal = {Nucleic Acids Research},
+	author = {Zhong, Cuncong and Tang, Haixu and Zhang, Shaojie},
+	month = oct,
+	year = {2010},
+	pages = {e176--e176},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/ESXL69Q6/Zhong et al. - 2010 - RNAMotifScan automatic identification of RNA stru.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/MWTNC94Z/1069222.html:text/html}
+}
+
+@inproceedings{tahi_fast_2003,
+	title = {A fast algorithm for {RNA} secondary structure prediction including pseudoknots},
+	doi = {10.1109/BIBE.2003.1188924},
+	abstract = {Many important RNA molecules contain pseudoknots, which are generally excluded by the definition of the secondary structure, mainly for computational reasons. Still, most existing algorithms for secondary structure prediction are not satisfactory in results and complexities, even when pseudoknots are not allowed. We present an algorithm, called P-DCFold, for the prediction of RNA secondary structures including all kinds of pseudoknots. It is based on the comparative approach. The helices are searched recursively, from more "likely" to less "likely", using the "Divide and Conquer" approach. This approach, which allows to limit the amount of searching, is possible when only non-interleaved helices are searched for. The pseudoknots are therefore searched in several steps, each helix of the pseudoknot being selected in a different step. P-DCFold has been applied to tmRNA and RnaseP sequences. In less than two seconds, their respective secondary structures, including their pseudoknots, have been recovered very efficiently.},
+	booktitle = {Third {IEEE} {Symposium} on {Bioinformatics} and {Bioengineering}, 2003. {Proceedings}.},
+	author = {Tahi, F. and Engelen, S. and Regnier, M.},
+	month = mar,
+	year = {2003},
+	keywords = {2 s, Bioinformatics, Biological control systems, computational methods, computational reasons, Context modeling, Databases, Evolution (biology), fast algorithm, macromolecules, molecular biophysics, molecular configurations, noninterleaved helices, Predictive models, pseudoknots, recursive searches, RNA, RNA secondary structure prediction, RnaseP, Robustness, secondary structures, spatial structures, Stochastic processes, Switches, tmRNA},
+	pages = {11--17},
+	file = {IEEE Xplore Abstract Record:/nhome/siniac/lbecquey/Zotero/storage/HTHXNSVF/1188924.html:text/html}
+}
+
+@article{tahi_p-dcfold_2005,
+	title = {P-dcfold or how to predict all kinds of pseudoknots in rna secondary structures},
+	volume = {14},
+	issn = {0218-2130},
+	url = {https://www.worldscientific.com/doi/abs/10.1142/S021821300500234X},
+	doi = {10.1142/S021821300500234X},
+	abstract = {Pseudoknots play important roles in many RNAs. But for computational reasons, pseudoknots are usually excluded from the definition of RNA secondary structures. Indeed, prediction of pseudoknots increase very highly the complexities in time of the algorithms, knowing that all existing algorithms for RNA secondary structure prediction have  complexities at least of O(n3). Some algorithms have  been developed for searching pseudoknots, but all of them have very high complexities, and consider generally particular kinds of pseudoknots.We present an algorithm, called P-DCFold based on the comparative approach, for the prediction of RNA secondary structures including all kinds of pseudoknots. The helices are searched recursively using the "Divide and Conquer" approach, searching the helices from the "most significant" to the "less significant". A selected  helix subdivide the sequence into two sub-sequences, the internal one and  a concatenation of the two externals. This approach is used to search  non-interleaved helices and allows to limit the space of searching. To  search for pseudoknots, the processing is reiterated. Therefore, each helix  of the pseudoknot is selected in a different step.P-DCFold has been applied to several RNA sequences. In less  than two seconds, their respective secondary structures, including their pseudoknots, have been recovered very efficiently.},
+	number = {05},
+	urldate = {2018-10-02},
+	journal = {International Journal on Artificial Intelligence Tools},
+	author = {Tahi, Fariza and Stefan, Engelen and Regnier, Mireille},
+	month = oct,
+	year = {2005},
+	pages = {703--716},
+	file = {Snapshot:/nhome/siniac/lbecquey/Zotero/storage/GEIBPMJ4/S021821300500234X.html:text/html}
+}
+
+@article{tempel_fast_2012,
+	title = {A fast ab-initio method for predicting {miRNA} precursors in genomes},
+	volume = {40},
+	issn = {0305-1048},
+	url = {https://academic.oup.com/nar/article/40/11/e80/2409259},
+	doi = {10.1093/nar/gks146},
+	abstract = {Abstract.   miRNAs are small non coding RNA structures which play important roles in biological processes. Finding miRNA precursors in genomes is therefore an i},
+	language = {en},
+	number = {11},
+	urldate = {2018-10-02},
+	journal = {Nucleic Acids Research},
+	author = {Tempel, Sébastien and Tahi, Fariza},
+	month = jun,
+	year = {2012},
+	pages = {e80--e80},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/BSCSRRL2/Tempel et Tahi - 2012 - A fast ab-initio method for predicting miRNA precu.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/ZTG4GDDT/2409259.html:text/html}
+}
+
+@article{reinharz_towards_2012,
+	title = {Towards 3D structure prediction of large {RNA} molecules: an integer programming framework to insert local 3D motifs in {RNA} secondary structure},
+	volume = {28},
+	issn = {1367-4803},
+	shorttitle = {Towards 3D structure prediction of large {RNA} molecules},
+	url = {https://academic.oup.com/bioinformatics/article/28/12/i207/269345},
+	doi = {10.1093/bioinformatics/bts226},
+	abstract = {Abstract.  Motivation: The prediction of RNA 3D structures from its sequence only is a milestone to RNA function analysis and prediction. In recent years, many},
+	language = {en},
+	number = {12},
+	urldate = {2018-10-01},
+	journal = {Bioinformatics},
+	author = {Reinharz, Vladimir and Major, François and Waldispühl, Jérôme},
+	month = jun,
+	year = {2012},
+	pages = {i207--i214},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/IAYRK53E/Reinharz et al. - 2012 - Towards 3D structure prediction of large RNA molec.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/SSMTN6YZ/269345.html:text/html}
+}
+
+@article{pan_predicting_nodate,
+	title = {Predicting {RNA}–protein binding sites and motifs through combining local and global deep convolutional neural networks},
+	url = {https://academic.oup.com/bioinformatics/advance-article/doi/10.1093/bioinformatics/bty364/4990826},
+	doi = {10.1093/bioinformatics/bty364},
+	abstract = {AbstractMotivation.  RNA-binding proteins (RBPs) take over 5–10\% of the eukaryotic proteome and play key roles in many biological processes, e.g. gene regulatio},
+	language = {en},
+	urldate = {2018-06-12},
+	journal = {Bioinformatics},
+	author = {Pan, Xiaoyong and Shen, Hong-Bin and Valencia, Alfonso},
+	file = {10.1093@bioinformatics@bty364.pdf:/nhome/siniac/lbecquey/Zotero/storage/KUQZ2HNN/10.1093@bioinformatics@bty364.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/TLQUYHEU/4990826.html:text/html}
+}
+
+@article{yi_brief_2017,
+	title = {A {Brief} {Review} of {RNA}–{Protein} {Interaction} {Database} {Resources}},
+	volume = {3},
+	issn = {2311-553X},
+	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5832006/},
+	doi = {10.3390/ncrna3010006},
+	abstract = {RNA–Protein interactions play critical roles in various biological processes. By collecting and analyzing the RNA–Protein interactions and binding sites from experiments and predictions, RNA–Protein interaction databases have become an essential resource for the exploration of the transcriptional and post-transcriptional regulatory network. Here, we briefly review several widely used RNA–Protein interaction database resources developed in recent years to provide a guide of these databases. The content and major functions in databases are presented. The brief description of database helps users to quickly choose the database containing information they interested. In short, these RNA–Protein interaction database resources are continually updated, but the current state shows the efforts to identify and analyze the large amount of RNA–Protein interactions.},
+	number = {1},
+	urldate = {2018-06-08},
+	journal = {Non-Coding RNA},
+	author = {Yi, Ying and Zhao, Yue and Huang, Yan and Wang, Dong},
+	month = jan,
+	year = {2017},
+	pmid = {29657278},
+	pmcid = {PMC5832006},
+	file = {PubMed Central Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/C3ZRG7MJ/Yi et al. - 2017 - A Brief Review of RNA–Protein Interaction Database.pdf:application/pdf}
+}
+
+@article{das_automated_2007,
+	title = {Automated de novo prediction of native-like {RNA} tertiary structures},
+	volume = {104},
+	copyright = {© 2007 by The National Academy of Sciences of the USA.                    Freely available online through the PNAS open access option.},
+	issn = {0027-8424, 1091-6490},
+	url = {http://www.pnas.org/content/104/37/14664},
+	doi = {10.1073/pnas.0703836104},
+	abstract = {RNA tertiary structure prediction has been based almost entirely on base-pairing constraints derived from phylogenetic covariation analysis. We describe here a complementary approach, inspired by the Rosetta low-resolution protein structure prediction method, that seeks the lowest energy tertiary structure for a given RNA sequence without using evolutionary information. In a benchmark test of 20 RNA sequences with known structure and lengths of ≈30 nt, the new method reproduces better than 90\% of Watson–Crick base pairs, comparable with the accuracy of secondary structure prediction methods. In more than half the cases, at least one of the top five models agrees with the native structure to better than 4 Å rmsd over the backbone. Most importantly, the method recapitulates more than one-third of non-Watson–Crick base pairs seen in the native structures. Tandem stacks of “sheared” base pairs, base triplets, and pseudoknots are among the noncanonical features reproduced in the models. In the cases in which none of the top five models were native-like, higher energy conformations similar to the native structures are still sampled frequently but not assigned low energies. These results suggest that modest improvements in the energy function, together with the incorporation of information from phylogenetic covariance, may allow confident and accurate structure prediction for larger and more complex RNA chains.},
+	language = {en},
+	number = {37},
+	urldate = {2018-06-04},
+	journal = {Proceedings of the National Academy of Sciences},
+	author = {Das, Rhiju and Baker, David},
+	month = sep,
+	year = {2007},
+	pmid = {17726102},
+	keywords = {ab initio, energy-based, fragment assembly, nucleic acid, Rosetta},
+	pages = {14664--14669},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/H79FEN6P/Das and Baker - 2007 - Automated de novo prediction of native-like RNA te.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/WH7PUGNW/14664.html:text/html}
+}
+
+@article{cao_physics-based_2011,
+	title = {Physics-based de novo prediction of {RNA} 3D structures},
+	volume = {115},
+	issn = {1520-6106},
+	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3072456/},
+	doi = {10.1021/jp112059y},
+	abstract = {Current experiments on structural determination cannot keep up the pace with the steadily emerging RNA sequences and new functions. This underscores the request for an accurate model for RNA three-dimensional (3D) structural prediction. Although considerable progress has been made in mechanistic studies, accurate prediction for RNA tertiary folding from sequence remains an unsolved problem. The first and most important requirement for the prediction of RNA structure from physical principles is an accurate free energy model. A recently developed three-vector virtual bond-based RNA folding model (“Vfold”) has allowed us to compute the chain entropy and predict folding free energies and structures for RNA secondary structures and simple pseudoknots. Here we develop a free energy-based method to predict larger more complex RNA tertiary folds. The approach is based on a multiscaling strategy: from the nucleotide sequence, we predict the two-dimensional (2D) structures (defined by the base pairs and tertiary contacts); based on the 2D structure, we construct a 3D scaffold; with the 3D scaffold as the initial state, we combine AMBER energy minimization and PDB-based fragment search to predict the all-atom structure. A key advantage of the approach is the statistical mechanical calculation for the conformational entropy of RNA structures, including those with cross-linked loops. Benchmark tests show that the model leads to significant improvements in RNA 3D structure prediction.},
+	number = {14},
+	urldate = {2018-06-04},
+	journal = {The journal of physical chemistry. B},
+	author = {Cao, Song and Chen, Shi-Jie},
+	month = apr,
+	year = {2011},
+	pmid = {21413701},
+	pmcid = {PMC3072456},
+	pages = {4216--4226},
+	file = {PubMed Central Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/ZY98QT5K/Cao and Chen - 2011 - Physics-based de novo prediction of RNA 3D structu.pdf:application/pdf}
+}
+
+@article{bottaro_towards_2015,
+	title = {Towards de novo {RNA} 3D {Structure} {Prediction}},
+	volume = {2},
+	copyright = {Copyright (c) 2015 Sandro Bottaro, Francesco Di Palma, Giovanni Bussi},
+	issn = {2375-2467},
+	url = {http://www.smartscitech.com/index.php/RD/article/view/544},
+	doi = {10.14800/rd.544},
+	abstract = {RNA is a fundamental class of biomolecules that mediate a large variety of molecular processes within the cell. Computational algorithms can be of great help in the understanding of RNA structure-function relationship. One of the main challenges in this field is the development of structure-prediction algorithms, which aim at the prediction of the three-dimensional (3D) native fold from the sole knowledge of the sequence. In a recent paper, we have introduced a scoring function for RNA structure prediction. Here, we analyze in detail the performance of the method, we underline strengths and shortcomings, and we discuss the results with respect to state-of-the-art techniques. These observations provide a starting point for improving current methodologies, thus paving the way to the advances of more accurate approaches for RNA 3D structure prediction.},
+	language = {en},
+	number = {2},
+	urldate = {2018-06-04},
+	journal = {RNA \& DISEASE},
+	author = {Bottaro, Sandro and Palma, Francesco Di and Bussi, Giovanni},
+	month = jan,
+	year = {2015},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/SWAYZQEV/Bottaro et al. - 2015 - Towards de novo RNA 3D Structure Prediction.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/SQMMYVCU/544.html:text/html}
+}
+
+@article{bindewald_multistrand_2016,
+	title = {Multistrand {Structure} {Prediction} of {Nucleic} {Acid} {Assemblies} and {Design} of {RNA} {Switches}},
+	volume = {16},
+	issn = {1530-6984},
+	url = {https://doi.org/10.1021/acs.nanolett.5b04651},
+	doi = {10.1021/acs.nanolett.5b04651},
+	abstract = {RNA is an attractive material for the creation of molecular logic gates that release programmed functionalities only in the presence of specific molecular interaction partners. Here we present HyperFold, a multistrand RNA/DNA structure prediction approach for predicting nucleic acid complexes that can contain pseudoknots. We show that HyperFold also performs competitively compared to other published folding algorithms. We performed a large variety of RNA/DNA hybrid reassociation experiments for different concentrations, DNA toehold lengths, and G+C content and find that the observed tendencies for reassociation correspond well to computational predictions. Importantly, we apply this method to the design and experimental verification of a two-stranded RNA molecular switch that upon binding to a single-stranded RNA toehold disease-marker trigger mRNA changes its conformation releasing an shRNA-like Dicer substrate structure. To demonstrate the concept, connective tissue growth factor (CTGF) mRNA and enhanced green fluorescent protein (eGFP) mRNA were chosen as trigger and target sequences, respectively. In vitro experiments confirm the formation of an RNA switch and demonstrate that the functional unit is being released when the trigger RNA interacts with the switch toehold. The designed RNA switch is shown to be functional in MDA-MB-231 breast cancer cells. Several other switches were also designed and tested. We conclude that this approach has considerable potential because, in principle, it allows the release of an siRNA designed against a gene that differs from the gene that is utilized as a biomarker for a disease state.},
+	number = {3},
+	urldate = {2018-05-31},
+	journal = {Nano Letters},
+	author = {Bindewald, Eckart and Afonin, Kirill A. and Viard, Mathias and Zakrevsky, Paul and Kim, Taejin and Shapiro, Bruce A.},
+	month = mar,
+	year = {2016},
+	pages = {1726--1735},
+	file = {ACS Full Text Snapshot:/nhome/siniac/lbecquey/Zotero/storage/285MME3I/acs.nanolett.html:text/html}
+}
+
+@article{ge_novo_2018,
+	title = {De novo discovery of structural motifs in {RNA} 3D structures through clustering},
+	volume = {46},
+	issn = {0305-1048},
+	url = {https://academic.oup.com/nar/article/46/9/4783/4925243},
+	doi = {10.1093/nar/gky139},
+	abstract = {Abstract.  As functional components in three-dimensional (3D) conformation of an RNA, the RNA structural motifs provide an easy way to associate the molecular a},
+	language = {en},
+	number = {9},
+	urldate = {2018-05-31},
+	journal = {Nucleic Acids Research},
+	author = {Ge, Ping and Islam, Shahidul and Zhong, Cuncong and Zhang, Shaojie},
+	month = may,
+	year = {2018},
+	pages = {4783--4793},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/8YS7LY6E/Ge et al. - 2018 - De novo discovery of structural motifs in RNA 3D s.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/4TLRV8ZT/4925243.html:text/html}
+}
+
+@article{wang_rna_2018,
+	title = {{RNA} 3-dimensional structural motifs as a critical constraint of viroid {RNA} evolution},
+	volume = {14},
+	issn = {1553-7374},
+	url = {http://journals.plos.org/plospathogens/article?id=10.1371/journal.ppat.1006801},
+	doi = {10.1371/journal.ppat.1006801},
+	language = {en},
+	number = {2},
+	urldate = {2018-05-31},
+	journal = {PLOS Pathogens},
+	author = {Wang, Ying and Zirbel, Craig L. and Leontis, Neocles B. and Ding, Biao},
+	month = feb,
+	year = {2018},
+	keywords = {Non-coding RNA sequences, RNA structure, RNA viruses, Sequence motif analysis, Viral evolution, Viral replication, Viral structure, Viroids},
+	pages = {e1006801},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/M3P6GCA7/Wang et al. - 2018 - RNA 3-dimensional structural motifs as a critical .pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/3YRBKI96/article.html:text/html}
+}
+
+@article{lorenz_viennarna_2011,
+	title = {{ViennaRNA} {Package} 2.0},
+	volume = {6},
+	issn = {1748-7188},
+	url = {https://doi.org/10.1186/1748-7188-6-26},
+	doi = {10.1186/1748-7188-6-26},
+	abstract = {Secondary structure forms an important intermediate level of description of nucleic acids that encapsulates the dominating part of the folding energy, is often well conserved in evolution, and is routinely used as a basis to explain experimental findings. Based on carefully measured thermodynamic parameters, exact dynamic programming algorithms can be used to compute ground states, base pairing probabilities, as well as thermodynamic properties.},
+	urldate = {2018-05-31},
+	journal = {Algorithms for Molecular Biology},
+	author = {Lorenz, Ronny and Bernhart, Stephan H. and Höner zu Siederdissen, Christian and Tafer, Hakim and Flamm, Christoph and Stadler, Peter F. and Hofacker, Ivo L.},
+	month = nov,
+	year = {2011},
+	keywords = {Consensus Structure, Folding Algorithm, Matthews Correlation Coefficient, Minimum Free Energy, Partition Function},
+	pages = {26},
+	annote = {Pages 26 in PDF},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/WFPBA2H8/Lorenz et al. - 2011 - ViennaRNA Package 2.0.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/ADNFF9EA/1748-7188-6-26.html:text/html}
+}
+
+@article{janssen_rna_2015,
+	title = {The {RNA} shapes studio},
+	volume = {31},
+	issn = {1367-4803},
+	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4308662/},
+	doi = {10.1093/bioinformatics/btu649},
+	abstract = {Motivation: Abstract shape analysis, first proposed in 2004, allows one to extract several relevant structures from the folding space of an RNA sequence, preferable to focusing in a single structure of minimal free energy. We report recent extensions to this approach., Results: We have rebuilt the original RNAshapes as a repository of components that allows us to integrate several established tools for RNA structure analysis: RNAshapes, RNAalishapes and pknotsRG, including its recent extension pKiss. As a spin-off, we obtain heretofore unavailable functionality: e. g. with pKiss, we can now perform abstract shape analysis for structures holding pseudoknots up to the complexity of kissing hairpin motifs. The new tool pAliKiss can predict kissing hairpin motifs from aligned sequences. Along with the integration, the functionality of the tools was also extended in manifold ways., Availability and implementation: As before, the tool is available on the Bielefeld Bioinformatics server at http://bibiserv.cebitec.uni-bielefeld.de/rnashapesstudio., Contact: bibi-help@cebitec.uni-bielefeld.de},
+	number = {3},
+	urldate = {2018-05-31},
+	journal = {Bioinformatics},
+	author = {Janssen, Stefan and Giegerich, Robert},
+	month = feb,
+	year = {2015},
+	pmid = {25273103},
+	pmcid = {PMC4308662},
+	pages = {423--425},
+	file = {PubMed Central Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/KFQTVDR3/Janssen and Giegerich - 2015 - The RNA shapes studio.pdf:application/pdf}
+}
+
+@article{parlea_rna_2016,
+	series = {Advances in {RNA} {Structure} {Determination}},
+	title = {The {RNA} 3D {Motif} {Atlas}: {Computational} methods for extraction, organization and evaluation of {RNA} motifs},
+	volume = {103},
+	issn = {1046-2023},
+	shorttitle = {The {RNA} 3D {Motif} {Atlas}},
+	url = {http://www.sciencedirect.com/science/article/pii/S1046202316301049},
+	doi = {10.1016/j.ymeth.2016.04.025},
+	abstract = {RNA 3D motifs occupy places in structured RNA molecules that correspond to the hairpin, internal and multi-helix junction “loops” of their secondary structure representations. As many as 40\% of the nucleotides of an RNA molecule can belong to these structural elements, which are distinct from the regular double helical regions formed by contiguous AU, GC, and GU Watson-Crick basepairs. With the large number of atomic- or near atomic-resolution 3D structures appearing in a steady stream in the PDB/NDB structure databases, the automated identification, extraction, comparison, clustering and visualization of these structural elements presents an opportunity to enhance RNA science. Three broad applications are: (1) identification of modular, autonomous structural units for RNA nanotechnology, nanobiology and synthetic biology applications; (2) bioinformatic analysis to improve RNA 3D structure prediction from sequence; and (3) creation of searchable databases for exploring the binding specificities, structural flexibility, and dynamics of these RNA elements. In this contribution, we review methods developed for computational extraction of hairpin and internal loop motifs from a non-redundant set of high-quality RNA 3D structures. We provide a statistical summary of the extracted hairpin and internal loop motifs in the most recent version of the RNA 3D Motif Atlas. We also explore the reliability and accuracy of the extraction process by examining its performance in clustering recurrent motifs from homologous ribosomal RNA (rRNA) structures. We conclude with a summary of remaining challenges, especially with regard to extraction of multi-helix junction motifs.},
+	urldate = {2018-05-31},
+	journal = {Methods},
+	author = {Parlea, Lorena G. and Sweeney, Blake A. and Hosseini-Asanjan, Maryam and Zirbel, Craig L. and Leontis, Neocles B.},
+	month = jul,
+	year = {2016},
+	keywords = {Hairpin loop, Internal loop, Multi-helix junction loop, Non-Watson-Crick basepair, RNA 3D Motif, Structured RNA molecules},
+	pages = {99--119},
+	file = {ScienceDirect Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/HM9ZDD83/Parlea et al. - 2016 - The RNA 3D Motif Atlas Computational methods for .pdf:application/pdf;ScienceDirect Snapshot:/nhome/siniac/lbecquey/Zotero/storage/ANJRICVQ/S1046202316301049.html:text/html}
+}
+
+@article{legendre_bi-objective_2018,
+	title = {Bi-objective integer programming for {RNA} secondary structure prediction with pseudoknots},
+	volume = {19},
+	issn = {1471-2105},
+	url = {https://doi.org/10.1186/s12859-018-2007-7},
+	doi = {10.1186/s12859-018-2007-7},
+	abstract = {RNA structure prediction is an important field in bioinformatics, and numerous methods and tools have been proposed. Pseudoknots are specific motifs of RNA secondary structures that are difficult to predict. Almost all existing methods are based on a single model and return one solution, often missing the real structure. An alternative approach would be to combine different models and return a (small) set of solutions, maximizing its quality and diversity in order to increase the probability that it contains the real structure.},
+	urldate = {2018-05-24},
+	journal = {BMC Bioinformatics},
+	author = {Legendre, Audrey and Angel, Eric and Tahi, Fariza},
+	month = jan,
+	year = {2018},
+	keywords = {RNA, Bi-objective, Integer programming, Optimal solutions, Pseudoknot, Secondary structure, Sub-optimal solutions},
+	pages = {13},
+	annote = {Pages 13 in PDF},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/4YMW5M4S/Legendre et al. - 2018 - Bi-objective integer programming for RNA secondary.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/XP46BMHH/s12859-018-2007-7.html:text/html}
+}
+
+@article{legendre_bi-objective_2018-1,
+	title = {Bi-objective integer programming for {RNA} secondary structure prediction with pseudoknots},
+	volume = {19},
+	issn = {1471-2105},
+	url = {https://doi.org/10.1186/s12859-018-2007-7},
+	doi = {10.1186/s12859-018-2007-7},
+	abstract = {RNA structure prediction is an important field in bioinformatics, and numerous methods and tools have been proposed. Pseudoknots are specific motifs of RNA secondary structures that are difficult to predict. Almost all existing methods are based on a single model and return one solution, often missing the real structure. An alternative approach would be to combine different models and return a (small) set of solutions, maximizing its quality and diversity in order to increase the probability that it contains the real structure.},
+	number = {1},
+	urldate = {2018-10-08},
+	journal = {BMC Bioinformatics},
+	author = {Legendre, Audrey and Angel, Eric and Tahi, Fariza},
+	month = jan,
+	year = {2018},
+	pages = {13},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/J36PRAPX/Legendre et al. - 2018 - Bi-objective integer programming for RNA secondary.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/BZCRBGLK/s12859-018-2007-7.html:text/html}
+}
+
+@article{sarver_fr3d:_2008,
+	title = {{FR}3D: finding local and composite recurrent structural motifs in {RNA} 3D structures},
+	volume = {56},
+	issn = {1432-1416},
+	shorttitle = {{FR}3D},
+	url = {https://doi.org/10.1007/s00285-007-0110-x},
+	doi = {10.1007/s00285-007-0110-x},
+	abstract = {New methods are described for finding recurrent three-dimensional (3D) motifs in RNA atomic-resolution structures. Recurrent RNA 3D motifs are sets of RNA nucleotides with similar spatial arrangements. They can be local or composite. Local motifs comprise nucleotides that occur in the same hairpin or internal loop. Composite motifs comprise nucleotides belonging to three or more different RNA strand segments or molecules. We use a base-centered approach to construct efficient, yet exhaustive search procedures using geometric, symbolic, or mixed representations of RNA structure that we implement in a suite of MATLAB programs, “Find RNA 3D” (FR3D). The first modules of FR3D preprocess structure files to classify base-pair and -stacking interactions. Each base is represented geometrically by the position of its glycosidic nitrogen in 3D space and by the rotation matrix that describes its orientation with respect to a common frame. Base-pairing and base-stacking interactions are calculated from the base geometries and are represented symbolically according to the Leontis/Westhof basepairing classification, extended to include base-stacking. These data are stored and used to organize motif searches. For geometric searches, the user supplies the 3D structure of a query motif which FR3D uses to find and score geometrically similar candidate motifs, without regard to the sequential position of their nucleotides in the RNA chain or the identity of their bases. To score and rank candidate motifs, FR3D calculates a geometric discrepancy by rigidly rotating candidates to align optimally with the query motif and then comparing the relative orientations of the corresponding bases in the query and candidate motifs. Given the growing size of the RNA structure database, it is impossible to explicitly compute the discrepancy for all conceivable candidate motifs, even for motifs with less than ten nucleotides. The screening algorithm that we describe finds all candidate motifs whose geometric discrepancy with respect to the query motif falls below a user-specified cutoff discrepancy. This technique can be applied to RMSD searches. Candidate motifs identified geometrically may be further screened symbolically to identify those that contain particular basepair types or base-stacking arrangements or that conform to sequence continuity or nucleotide identity constraints. Purely symbolic searches for motifs containing user-defined sequence, continuity and interaction constraints have also been implemented. We demonstrate that FR3D finds all occurrences, both local and composite and with nucleotide substitutions, of sarcin/ricin and kink-turn motifs in the 23S and 5S ribosomal RNA 3D structures of the H. marismortui 50S ribosomal subunit and assigns the lowest discrepancy scores to bona fide examples of these motifs. The search algorithms have been optimized for speed to allow users to search the non-redundant RNA 3D structure database on a personal computer in a matter of minutes.},
+	language = {en},
+	number = {1},
+	urldate = {2018-10-10},
+	journal = {Journal of Mathematical Biology},
+	author = {Sarver, Michael and Zirbel, Craig L. and Stombaugh, Jesse and Mokdad, Ali and Leontis, Neocles B.},
+	month = jan,
+	year = {2008},
+	keywords = {05C85, 92C40},
+	pages = {215--252}
+}
+
+@article{petrov_webfr3dserver_2011,
+	title = {{WebFR}3D—a server for finding, aligning and analyzing recurrent {RNA} 3D motifs},
+	volume = {39},
+	issn = {0305-1048},
+	url = {https://academic.oup.com/nar/article/39/suppl_2/W50/2505799},
+	doi = {10.1093/nar/gkr249},
+	abstract = {Abstract.   WebFR3D is the on-line version of ‘Find RNA 3D’ (FR3D), a program for annotating atomic-resolution RNA 3D structure files and searching them efficie},
+	language = {en},
+	number = {suppl\_2},
+	urldate = {2018-10-10},
+	journal = {Nucleic Acids Research},
+	author = {Petrov, Anton I. and Zirbel, Craig L. and Leontis, Neocles B.},
+	month = jul,
+	year = {2011},
+	pages = {W50--W55},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/WVGVFLFH/Petrov et al. - 2011 - WebFR3D—a server for finding, aligning and analyzi.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/8NMZZLKV/2505799.html:text/html}
+}
+
+@article{petrov_automated_2013,
+	title = {Automated classification of {RNA} 3D motifs and the {RNA} 3D {Motif} {Atlas}},
+	volume = {19},
+	issn = {1355-8382, 1469-9001},
+	url = {http://rnajournal.cshlp.org/content/19/10/1327},
+	doi = {10.1261/rna.039438.113},
+	abstract = {A monthly journal publishing high-quality, peer-reviewed research on all topics related to RNA and its metabolism in all organisms},
+	language = {en},
+	number = {10},
+	urldate = {2018-10-10},
+	journal = {RNA},
+	author = {Petrov, Anton I. and Zirbel, Craig L. and Leontis, Neocles B.},
+	month = jan,
+	year = {2013},
+	pmid = {23970545},
+	pages = {1327--1340},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/GIC5F2CJ/Petrov et al. - 2013 - Automated classification of RNA 3D motifs and the .pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/UJFVEML3/1327.full.html:text/html}
+}
+
+@article{lu_dssr:_2015,
+	title = {{DSSR}: an integrated software tool for dissecting the spatial structure of {RNA}},
+	volume = {43},
+	issn = {0305-1048},
+	shorttitle = {{DSSR}},
+	url = {https://academic.oup.com/nar/article/43/21/e142/2468098},
+	doi = {10.1093/nar/gkv716},
+	abstract = {Abstract.  Insight into the three-dimensional architecture of RNA is essential for understanding its cellular functions. However, even the classic transfer RNA},
+	language = {en},
+	number = {21},
+	urldate = {2018-10-09},
+	journal = {Nucleic Acids Research},
+	author = {Lu, Xiang-Jun and Bussemaker, Harmen J. and Olson, Wilma K.},
+	month = dec,
+	year = {2015},
+	pages = {e142--e142},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/NURMS9UY/Lu et al. - 2015 - DSSR an integrated software tool for dissecting t.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/BTZXBR6S/2468098.html:text/html}
+}
+
+@article{antczak_rnapdbeewebserver_2014,
+	title = {{RNApdbee}—a webserver to derive secondary structures from pdb files of knotted and unknotted {RNAs}},
+	volume = {42},
+	issn = {0305-1048},
+	url = {https://academic.oup.com/nar/article/42/W1/W368/2435287},
+	doi = {10.1093/nar/gku330},
+	abstract = {Abstract.  In RNA structural biology and bioinformatics an access to correct RNA secondary structure and its proper representation is of crucial importance. Thi},
+	language = {en},
+	number = {W1},
+	urldate = {2018-10-09},
+	journal = {Nucleic Acids Research},
+	author = {Antczak, Maciej and Zok, Tomasz and Popenda, Mariusz and Lukasiak, Piotr and Adamiak, Ryszard W. and Blazewicz, Jacek and Szachniuk, Marta},
+	month = jul,
+	year = {2014},
+	pages = {W368--W372},
+	file = {Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/RWXNJQH6/Antczak et al. - 2014 - RNApdbee—a webserver to derive secondary structure.pdf:application/pdf;Snapshot:/nhome/siniac/lbecquey/Zotero/storage/H6CZVH4F/2435287.html:text/html}
+}
+
+@article{laing_computational_2010,
+	title = {Computational approaches to 3D modeling of {RNA}},
+	volume = {22},
+	issn = {0953-8984},
+	url = {http://stacks.iop.org/0953-8984/22/i=28/a=283101},
+	doi = {10.1088/0953-8984/22/28/283101},
+	abstract = {Many exciting discoveries have recently revealed the versatility of RNA and its importance in a variety of functions within the cell. Since the structural features of RNA are of major importance to their biological function, there is much interest in predicting RNA structure, either in free form or in interaction with various ligands, including proteins, metabolites and other molecules. In recent years, an increasing number of researchers have developed novel RNA algorithms for predicting RNA secondary and tertiary structures. In this review, we describe current experimental and computational advances and discuss recent ideas that are transforming the traditional view of RNA folding. To evaluate the performance of the most recent RNA 3D folding algorithms, we provide a comparative study in order to test the performance of available 3D structure prediction algorithms for an RNA data set of 43 structures of various lengths and motifs. We find that the algorithms vary widely in terms of prediction quality across different RNA lengths and topologies; most predictions have very large root mean square deviations from the experimental structure. We conclude by outlining some suggestions for future RNA folding research.},
+	language = {en},
+	number = {28},
+	urldate = {2018-10-09},
+	journal = {Journal of Physics: Condensed Matter},
+	author = {Laing, Christian and Schlick, Tamar},
+	year = {2010},
+	pages = {283101}
+}
+
+@article{dawson_computational_2016,
+	series = {Theory and simulation • {Macromolcular} machines},
+	title = {Computational modeling of {RNA} 3D structures and interactions},
+	volume = {37},
+	issn = {0959-440X},
+	url = {http://www.sciencedirect.com/science/article/pii/S0959440X15001700},
+	doi = {10.1016/j.sbi.2015.11.007},
+	abstract = {RNA molecules have key functions in cellular processes beyond being carriers of protein-coding information. These functions are often dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is difficult, which has prompted the development of computational methods for structure prediction from sequence. Recent progress in 3D structure modeling of RNA and emerging approaches for predicting RNA interactions with ions, ligands and proteins have been stimulated by successes in protein 3D structure modeling.},
+	urldate = {2018-10-09},
+	journal = {Current Opinion in Structural Biology},
+	author = {Dawson, Wayne K and Bujnicki, Janusz M},
+	month = apr,
+	year = {2016},
+	pages = {22--28},
+	file = {ScienceDirect Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/7V5SQ8PN/Dawson et Bujnicki - 2016 - Computational modeling of RNA 3D structures and in.pdf:application/pdf;ScienceDirect Snapshot:/nhome/siniac/lbecquey/Zotero/storage/CDMTYU7W/S0959440X15001700.html:text/html}
+}
+
+@article{laing_computational_2011,
+	title = {Computational approaches to {RNA} structure prediction, analysis, and design},
+	volume = {21},
+	issn = {0959-440X},
+	url = {http://www.sciencedirect.com/science/article/pii/S0959440X11000674},
+	doi = {10.1016/j.sbi.2011.03.015},
+	abstract = {RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires RNA tertiary structure knowledge. Although modeling approaches for the study of RNA structures and dynamics lag behind efforts in protein folding, much progress has been achieved in the past two years. Here, we review recent advances in RNA folding algorithms, RNA tertiary motif discovery, applications of graph theory approaches to RNA structure and function, and in silico generation of RNA sequence pools for aptamer design. Advances within each area can be combined to impact many problems in RNA structure and function.},
+	number = {3},
+	urldate = {2018-10-09},
+	journal = {Current Opinion in Structural Biology},
+	author = {Laing, Christian and Schlick, Tamar},
+	month = jun,
+	year = {2011},
+	pages = {306--318},
+	file = {ScienceDirect Snapshot:/nhome/siniac/lbecquey/Zotero/storage/LWS5RU5Z/S0959440X11000674.html:text/html}
+}
+
+@article{sato_ipknot:_2011,
+	title = {{IPknot}: fast and accurate prediction of {RNA} secondary structures with pseudoknots using integer programming},
+	volume = {27},
+	issn = {1367-4803},
+	shorttitle = {{IPknot}},
+	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3117384/},
+	doi = {10.1093/bioinformatics/btr215},
+	abstract = {Motivation: Pseudoknots found in secondary structures of a number of functional RNAs play various roles in biological processes. Recent methods for predicting RNA secondary structures cover certain classes of pseudoknotted structures, but only a few of them achieve satisfying predictions in terms of both speed and accuracy., Results: We propose IPknot, a novel computational method for predicting RNA secondary structures with pseudoknots based on maximizing expected accuracy of a predicted structure. IPknot decomposes a pseudoknotted structure into a set of pseudoknot-free substructures and approximates a base-pairing probability distribution that considers pseudoknots, leading to the capability of modeling a wide class of pseudoknots and running quite fast. In addition, we propose a heuristic algorithm for refining base-paring probabilities to improve the prediction accuracy of IPknot. The problem of maximizing expected accuracy is solved by using integer programming with threshold cut. We also extend IPknot so that it can predict the consensus secondary structure with pseudoknots when a multiple sequence alignment is given. IPknot is validated through extensive experiments on various datasets, showing that IPknot achieves better prediction accuracy and faster running time as compared with several competitive prediction methods., Availability: The program of IPknot is available at http://www.ncrna.org/software/ipknot/. IPknot is also available as a web server at http://rna.naist.jp/ipknot/., Contact: satoken@k.u-tokyo.ac.jp; ykato@is.naist.jp, Supplementary information: Supplementary data are available at Bioinformatics online.},
+	number = {13},
+	urldate = {2018-10-12},
+	journal = {Bioinformatics},
+	author = {Sato, Kengo and Kato, Yuki and Hamada, Michiaki and Akutsu, Tatsuya and Asai, Kiyoshi},
+	month = jul,
+	year = {2011},
+	pmid = {21685106},
+	pmcid = {PMC3117384},
+	pages = {i85--i93},
+	file = {Texte intégral:/nhome/siniac/lbecquey/Zotero/storage/EEWT77EA/Sato et al. - 2011 - IPknot fast and accurate prediction of RNA second.pdf:application/pdf}
+}
+
+@article{zirbel_identifying_2015,
+	title = {Identifying novel sequence variants of {RNA} 3D motifs},
+	volume = {43},
+	issn = {0305-1048},
+	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4551918/},
+	doi = {10.1093/nar/gkv651},
+	abstract = {Predicting RNA 3D structure from sequence is a major challenge in biophysics. An important sub-goal is accurately identifying recurrent 3D motifs from RNA internal and hairpin loop sequences extracted from secondary structure (2D) diagrams. We have developed and validated new probabilistic models for 3D motif sequences based on hybrid Stochastic Context-Free Grammars and Markov Random Fields (SCFG/MRF). The SCFG/MRF models are constructed using atomic-resolution RNA 3D structures. To parameterize each model, we use all instances of each motif found in the RNA 3D Motif Atlas and annotations of pairwise nucleotide interactions generated by the FR3D software. Isostericity relations between non-Watson–Crick basepairs are used in scoring sequence variants. SCFG techniques model nested pairs and insertions, while MRF ideas handle crossing interactions and base triples. We use test sets of randomly-generated sequences to set acceptance and rejection thresholds for each motif group and thus control the false positive rate. Validation was carried out by comparing results for four motif groups to RMDetect. The software developed for sequence scoring (JAR3D) is structured to automatically incorporate new motifs as they accumulate in the RNA 3D Motif Atlas when new structures are solved and is available free for download.},
+	number = {15},
+	urldate = {2018-10-19},
+	journal = {Nucleic Acids Research},
+	author = {Zirbel, Craig L. and Roll, James and Sweeney, Blake A. and Petrov, Anton I. and Pirrung, Meg and Leontis, Neocles B.},
+	month = sep,
+	year = {2015},
+	pmid = {26130723},
+	pmcid = {PMC4551918},
+	pages = {7504--7520},
+	file = {PubMed Central Full Text PDF:/nhome/siniac/lbecquey/Zotero/storage/C68JKL5J/Zirbel et al. - 2015 - Identifying novel sequence variants of RNA 3D moti.pdf:application/pdf}
+}
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+\documentclass{article}
+\usepackage[utf8]{inputenc}
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+\usepackage{multirow}	
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+\usepackage{titlesec}
+\usepackage{enumitem}
+\usepackage{notoccite}
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+\titlespacing*{\itemize}{0pt}{0pt plus 0pt minus 0pt}{0pt plus 0pt minus 0pt}
+
+\title{Intermediate Work Report:}
+\author{Louis Becquey}
+\date{\today}
+
+\setlength\parskip{\baselineskip}
+
+\pagestyle{fancy}
+\setlength{\headheight}{14.7pt}
+\fancyhead[L]{\textsc{IP framework inserting RNA motives}}
+% \fancyhead[L]{\leftmark}
+\fancyhead[R]{Louis Becquey}
+\fancyfoot[L]{}
+\fancyfoot[C]{}
+\fancyfoot[R]{\thepage}
+\begin{document}
+
+\begin{titlepage}
+	\AddToShipoutPicture*{\BackgroundPic}
+	\begin{center}
+		\vspace{3cm}
+		\LARGE
+		\textsc{Intermediate Work Report:}\\
+		{\Large Louis Becquey, \today}\\
+		\vspace{2cm}
+		\textit{An IP framework that uses detected possible RNA motifs\\ to predict RNA secondary structures}\\
+	\end{center}
+	\normalsize
+	\vspace{5cm}
+	
+	\hrulefill
+	\flushright{		
+		\textbf{under the supervision of:\\}
+			Fariza Tahi, HDR \\
+			Eric Angel, HDR \\
+			\textit{AROBAS, IBISC, Paris-Saclay University}\\
+			~ \\
+			\includegraphics[height=1cm]{logoIBISC.png} ~ ~ 
+			\includegraphics[height=1cm]{minisaclay.png}
+	}
+	\flushleft
+	\hrulefill
+	\tableofcontents
+\end{titlepage}
+				
+\newpage
+\section{Motivation}
+We now have quite consistent RNA motif databases (RNA3Dmotif \cite{djelloul_automated_2008}, the RNA Motif Atlas \cite{petrov_automated_2013}).\\
+We call a RNA motif the combined description of these points:
+\begin{itemize}
+	\item A sequence or consensus sequence that we know to adopt a particular base-pairing organisation (sequence information),
+	\item A particular base-pairing pattern in this sequence (or consensus sequence) considering canonical \& wobble pairing (bi-dimensional information),
+	\item A particular organisation of non-canonical contacts in space (tri-dimensional information).
+\end{itemize}
+Then, a RNA motif is direct data about how a sequence can fold in space. Here, we are interested in using them to predict the bi or tri dimensional structure of an RNA sequence from scratch. 
+Then, the algorithm we plan to use is the following:
+	
+\begin{itemize}
+	\item Find all possible occurences of known RNA motifs in the query sequence by pattern matching of the motifs consensus sequences against the query bases,
+	\item Define constraints on the secondary structure imposed by motives if included
+	\item Find a secondary structure that satisfies both the most the expected accuracy (MEA model) and criterion of motif inclusion, by solving a bi-objective IP problem, using the previous constraints.
+\end{itemize}
+
+\newpage
+\section{Pattern matching to detect motif sites}
+A very complete model has been developped by the BGSU team \cite{zirbel_identifying_2015}, 
+which perfectly suits this need: JAR3D finds, given a RNA sequence with no additional information, 
+the sites that are likely to fold in known 3D motives of the RNA Motif Atlas \cite{petrov_automated_2013}.
+
+The RNA 3D Motif Atlas is an updated database of substructures exracted from a non-redundant set of 3D RNA structures. They are grouped into "motifs", which are a given pattern of 3D non-canonical interactions.
+Each motif contains one or several instances observed in real RNA structures. 
+The instances might differ in sequence, length of bulged insertions, and other details, but share a common graph of 3D non-canonical interactions.
+
+For each motif group of the database, JAR3D estimates the probability that a sequence folds into the 3D pattern, given the known members of the motif group. It takes into account crossed contacts, base-ribose and base-phosphate interactions, and triple base-pairs.
+
+This is the most scientifically correct approach to use to my knowledge. Unfortunately, the code is in MatLab and seems hard to use on a single computer (JAR3D is basically a webserver).
+
+\section{Formulation of the IP problem}
+	
+This formulation is an improved merge between the IPknot \cite{sato_ipknot:_2011} formulation (without "levels") and RNAMoIP's one \cite{reinharz_towards_2012}.
+% This problem has been inspired by IPknot's model \cite{sato_ipknot:_2011}, but without the use of what they call \textit{levels}, which are pseudoknot-free
+% structures that should be superposed to give the true pseudoknotted secondary structure graph.\\
+% Levels are mutually exclusive (a base cannot be paired in two different levels). The more levels you use, the more decision variables you have, 
+% but the more complex pseudoknots you are able to predict. IPknot and BiokoP use 2 levels, to predict simple knots.\\
+% \begin{figure}[h]\centering \includegraphics[height=5cm]{levels.png}\end{figure}
+	
+	
+\subsection{Variables} 
+	
+% Let $m$ be the number of levels that our program uses.\\
+Let $n$ be the number of nucleotides in the query RNA sequence $s$.\\
+Let $M$ be the set of motifs that could be inserted in $s$ (a match exist between $s$ and the sequence of the motifs' components).\\
+Let $x$ be a motif of $M$, $x$ having $j^x$ distinct components.\\
+Let $P_{x,i}$ be the set of positions in $s$ where we can insert the $i$th component of motif $x$.\\
+Let $k_{x,i}$ be the size in nucleotides of that $i$th component of $x$.\\
+Let $y^u_v$ be the \textbf{decision boolean variable} indicating that $s[u]$ and $s[v]$ form a canonical base pairing. Then, we always have $u \neq v$.\\
+Let $C^{x,i}_p$ be the \textbf{decision boolean variable} indicating that we do insert the $i$th component of motif $x$ at position $p$.
+	
+	
+Note that a base pair $y^u_v$ is possible if and only if $v>u+3$, and that we do not need to use two variables $y^u_v$ and $y_{vu}$ for the same pair. 
+Then, we have $\sum_{i=4}^n (n-i)$ decision variables ($\approx \frac{1}{2}n^2$ decision variables) of the form $y^u_v$.
+Regarding the $C^{x,i}_p$, if we have an average insertion of $\nu$ motives by RNA sequence, the motives having in average $\mu$ components, components that can be inserted in average at $\pi$ different positions in $s$,
+then we need to add, in average, $\nu \times \mu \times \pi$ decision variables $C^{x,i}_p$.
+
+Then, we expect having around $\frac{1}{2}n^2+\nu \mu \pi$ decision variables.
+
+\newpage
+\subsection{Objectives}
+We have two objectives : Find a structure with correct expected accuracy, and find a structure which includes (large) known motifs.
+Let $X$ be the vector of all our decision variables, we define the following loss functions to maximize:
+$$ f_1(X) = \sum_{x \in M} \left[ (j^x)^2 \times \sum_{p \in P_{x,1}} C^{x,1}_p \right]$$
+$$ f_2(X) = \sum_{u<v} p_{uv}\times y^u_v \times I[p_{uv}>\theta], \qquad \qquad
+p_{uv} = \sum_{\sigma \in S(s)} y^u_v.p(\sigma | s)$$
+$f_1$ is supposed to maximize the number of inserted motives in $s$, weighted by their number of components.
+$f_2$ is supposed to maximise the expected accuracy of the secondary structure (MEA model). 
+$p_{uv}$ are the base pairing probabilities that can be estimated from a set $S(s)$ of secondary structures of $s$.
+
+\subsection{10 Constraints to bind them all}
+\paragraph{Constraint to ensure there only is 0 or 1 canonical pairing by nucleotide} ~ 
+\begin{equation} \label{constraint:1}
+	\sum_{v>u} y^u_v + \sum_{v<u} y^v_u \leq 1 \qquad\qquad \forall u \in \llbracket 1,n \rrbracket
+\end{equation}
+	
+\paragraph{Constraints to forbid lonely base pairs} ~
+\begin{equation} \label{constraint:2}
+	1 + \sum_{v=u}^n y^{u-1}_v - \sum_{v=u+1}^n y^u_v + \sum_{v=u+2}^n y^{u+1}_v \geq 1 \qquad \qquad \forall u \in \llbracket 1,n\rrbracket
+\end{equation}
+\begin{equation} \label{constraint:3}
+	1 + \sum_{u=1}^{v-2} y^u_{v-1} - \sum_{u=1}^{v-1} y^u_v + \sum_{u=1}^{v} y^u_{v+1} \geq 1 \qquad \qquad \forall v \in \llbracket 1,n\rrbracket
+\end{equation}
+These conditions ensure that if a base pair exists with $s[i]$, 
+one of the adjacent bases is paired too. 
+Equation \ref{constraint:2} is useful if $s[u]$ is paired with $s[v>u]$ (a nucleotide later in the sequence), 
+and equation \ref{constraint:3} if $s[v]$ is paired with $s[u<v]$ (a nucleotide earlier in the sequence).
+	
+\paragraph{Constraint to forbid pairings inside a motif component} ~ 
+\begin{equation} \label{constraint:4}
+	k_{x,i} \; C^{x,i}_p + \sum_{u=p}^{p+k_{x,i}-1}\left[ \sum_{v>u} y^u_v + \sum_{v<u} y^v_u \right] \leq k_{x,i} 
+	\qquad \qquad \forall p \in P_{x,i} \qquad \forall x \in M, i \in \llbracket 1,j^x \rrbracket
+\end{equation}
+	
+\paragraph{Constraint to forbid component to overlap} ~
+\begin{equation} \label{constraint:5}
+	\sum_{x \in M} \sum_{i=1}^{j^x}\sum_{\substack{p \in P_{x,i}\\u-k_{x,i}+1 \leq p \leq u}}^u C^{x,i}_p \leq 1 \qquad \qquad \forall u \in \llbracket 1,n \rrbracket
+\end{equation}
+Then, whatever the nucleotide $u$, it can be part of a motif component only once. 
+$u$ belongs to a component $x,i$ if and only if $u-k_{x,i}+1 \leq p_{x,i} \leq u$.\\
+\begin{center}\includegraphics[height=3cm]{component.png}\end{center}
+	
+\paragraph{Constraints to respect the structure of large motives ($\forall x \in \{ x\in M | j^x \geq 2\}$)} ~ 
+
+The first two constraints ensure that a component is inserted if and only if the next and the previous one are also inserted somewhere.
+They also force a minimal distance of 3 nucleotides between any two consecutive components of the same motif.
+\begin{equation}\label{constraint:6}
+	C^{x,i}_p \leq \sum_{\substack{p' \in P_{x,i+1}\\ p'>p+k_{x,i}+2}} C^{x,i+1}_{p'}	
+	\qquad \qquad \forall p \in P_{x,i} \qquad \forall x \in \{ x\in M | j^x \geq 2\}, i \in \llbracket 1,j^x \llbracket
+\end{equation}
+\begin{equation}\label{constraint:7}
+	C^{x,i}_p \leq \sum_{\substack{p' \in P_{x,i-1}\\ p'<p-k_{x,i-1}-2}} C^{x,i-1}_{p'}	
+	\qquad \qquad \forall p \in P_{x,i} \qquad \forall x \in \{ x\in M | j^x \geq 2\}, i \in \rrbracket 1,j^x \rrbracket
+\end{equation}
+We add another one to ensure that all components of any motif are inserted the same number of times in $s$:
+\begin{equation}\label{constraint:8}
+	\sum_{p\in P_{x,1}} C^{x,1}_p - \frac{1}{j^x} \sum_{i=1}^{j^x} \sum_{p\in P_{x,i}} C^{x,i}_p = 0  \qquad \qquad x\in M
+\end{equation}
+And finally, we force base pairs between the end of a component and the beginning of the next one:
+\begin{equation}\label{constraint:9}
+	C^{x,i}_p \leq \sum_{p' \in P_{x,i-1}} y^{p'+k_{x,i}-1}_p \qquad \qquad \forall x \in \{ x\in M | j^x \geq 2\}, i \in \rrbracket 1,j^x \rrbracket
+\end{equation}
+\begin{equation}\label{constraint:10}
+	C^{x,i}_p \leq \sum_{p' \in P_{x,i+1}} y^{p+k_{x,i}-1}_{p'} \qquad \qquad \forall x \in \{ x\in M | j^x \geq 2\}, i \in \llbracket 1,j^x \llbracket
+\end{equation}
+
+\section{Remaning questions}
+	\begin{itemize}
+		\item I am not sure how to compute the base-pair probabilities for the MEA model (objective $f_2$). 
+		If you already have a set of secondary structures $S(s)$, why do you need this program ?
+		\item In objective $f_1$, weighting the motif by the number of components (squared) shows no reason to be the best idea. 
+		Some exploration is needed. An additional weight given by the pattern-matching step might be an idea, reflecting the probability to see the motif here in $s$.
+		
+	\end{itemize}
+	
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \newpage
+\bibliographystyle{unsrt}
+\bibliography{RNA}
+\end{document}
\ No newline at end of file

+>All values represent delta G in units of deka cal/mol (kcal/mol*100)
+>Stacking 5' X1 Y1 3'
+>         3' X2 Y2 5'
+>X1X2 = AU CG GC UA GU UG (row headings)
+>Y1Y2 = AU CG GC UA GU UG (column headings)
+ -90 -220 -210 -110  -60 -140 
+-210 -330 -240 -210 -140 -210 
+-240 -340 -330 -220 -150 -250 
+-130 -240 -210  -90 -100 -130 
+-130 -250 -210 -140  -50  130 
+-100 -150 -140  -60   30  -50 
+>Hairpin Loop Energies: size = 1,2,3,..,30
+   0    0  570  560  560  540  590  560  640  650  660  670  680  690  690  700  710  710  720  720  730  730  740  740  750  750  750  760  760  770 
+>Bulge loop Energies: size = 1,2,3,..,30
+ 380  280  320  360  400  440  460  470  480  490  500  510  520  530  540  540  550  550  560  570  570  580  580  580  590  590  600  600  600  610 
+>Interior Loop Energies: size = 1,2,3,..,30
+   0    0    0  170  180  200  220  230  240  250  260  270  280  290  300  300  310  310  320  330  330  340  340  340  350  350  360  360  360  370 
+>NINIO asymmetry Terms: m1, m2, m3, m4, max
+>Energy = MAX[ max, asymmetry*m#] where # = MIN(4,L1,L2)
+>and L1, L2 are lengths of each side of loop, 
+>and asymmetry = |L1-L2|
+  50   50   50   50  300
+>Triloops  5' .. 3' (Not listed equals 0 bonus)
+AAAAU     0
+>Tetraloops  5' .. 3' (Not listed equals 0 bonus)
+AGAAAU -200
+AGCAAU -150
+AGUAAU -150
+AGUGAU -150
+CGAAAG -300
+CGAAGG -250
+CGAGAG -200
+CGCAAG -300
+CGCGAG -250
+CGGAAG -300
+CGGGAG -150
+CGUAAG -200
+CGUGAG -300
+CUAACG -200
+CUACGG -250
+CUUCGG -300
+GGAAAC -300
+GGAAGC -150
+GGAGAC -300
+GGCAAC -250
+GGCGAC -150
+GGGAAC -150
+GGGAGC -150
+GGGGAC -300
+GGUGAC -300
+GUGAAC -150
+UGAAAA -150
+UGAAAG -200
+UGAGAG -250
+UGGAAA -150
+>Mismatch HP:
+>Columns 5'-AU,CG,GC,UA,GU,UG-3'
+>rows 5'-AA,AC,AG,AU,CA,..,UU-3'
+ -30 -150 -110  -50   20  -50 
+ -50 -150 -150  -30  -50  -30 
+ -30 -140 -130  -60  -30  -60 
+ -30 -180 -210  -50  -30  -50 
+ -10 -100 -110  -20  -10  -20 
+ -20  -90  -70  -10  -20  -10 
+-150 -290 -240 -120 -150 -170 
+ -20  -80  -50    0  -20    0 
+-110 -220 -240 -140  -90  -80 
+-120 -200 -290 -120 -110 -120 
+ -20 -160 -140  -70  -30  -30 
+  20 -110 -120  -20    0  -70 
+ -30 -170 -190  -30  -30  -60 
+ -30 -140 -100  -10  -30  -10 
+ -60 -180 -220  -50  -40  -60 
+-110 -200 -150  -80 -110  -80 
+>Mismatch Interior:
+>Columns 5'-AU,CG,GC,UA,GU,UG-3'
+>rows 5'-AA,AC,AG,AU,CA,..,UU-3'
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+ -40 -110 -110  -40  -40  -40 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+ -40 -110 -110  -40  -40  -40 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+  70    0    0   70   70   70 
+   0  -70  -70    0    0    0 
+>Dangle Energies: 5' X1 Y 3'
+>                 3' X2 . 5'
+>Columns: Y = A, C, G, U
+>Rows = X1X2 = AU,CG,GC,UA,GU,UG
+ -80  -50  -80  -60 
+-170  -80 -170 -120 
+-110  -40 -130  -60 
+ -70  -10  -70  -10 
+ -80  -50  -80  -60 
+ -70  -10  -70  -10 
+>Dangle Energies: 5' X1 . 3'
+>                 3' X2 Y 5'
+>Columns: Y = A, C, G, U
+>Rows = X1X2 = AU,CG,GC,UA,GU,UG
+ -30  -10  -20  -20 
+ -20  -30    0    0 
+ -50  -30  -20  -10 
+ -30  -30  -40  -20 
+ -30  -10  -20  -20 
+ -30  -30  -40  -20 
+>Multiloop terms: ALPHA_1, ALPHA_2, ALPHA_3
+>ML penalty = ALPHA_1 + s * ALPHA_2 + u *ALPHA_3
+>s = # stems adjacent to ML, u = unpaired bases in ML
+ 340   40    0
+>AT_PENALTY: 
+>Penalty for non GC pairs that terminate a helix
+  50
+>Interior Loops 1x1
+>CG..AU = 5'- C X A 3'
+>         3'- G Y U 5'
+>Rows: X = A C G U (X constant for a row)
+>Columns: Y = A C G U (Y constant in column)
+AU..AU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  150 
+AU..CG
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  100 
+AU..GC
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+AU..UA
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  120 
+AU..GU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+AU..UG
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+CG..AU
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+CG..CG
+  40  -40   40   40 
+  30   50   40   50 
+ -10   40 -170   40 
+  40    0   40  -30 
+CG..GC
+ 110   40   40   40 
+  40   40   40   40 
+  40   40 -140   40 
+  40   40   40   40 
+CG..UA
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+CG..GU
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+CG..UG
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+GC..AU
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+GC..CG
+  80   40   40   40 
+  40   40   40   40 
+  40   40 -210   40 
+  40   40   40  -70 
+GC..GC
+  40   30  -10   40 
+ -40   50   40    0 
+  40   40 -170   40 
+  40   50   40  -30 
+GC..UA
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  100 
+GC..GU
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+GC..UG
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+UA..AU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  180 
+UA..CG
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+UA..GC
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+UA..UA
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  150 
+UA..GU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+UA..UG
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+GU..AU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+GU..CG
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+GU..GC
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+GU..UA
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+GU..GU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+GU..UG
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+UG..AU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+UG..CG
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+UG..GC
+ 110  110  110  110 
+ 110  110  110  110 
+ 110  110 -100  110 
+ 110  110  110  110 
+UG..UA
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+UG..GU
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+UG..UG
+ 170  170  170  170 
+ 170  170  170  170 
+ 170  170  -40  170 
+ 170  170  170  170 
+>Interior Loops 2x2
+>CG.AG..AU = 5'- C A G A -3'
+>            3'- G Y X U -5'
+>Rows: X = A C G U (X constant for a row)
+>Columns: Y = A C G U (Y constant in column)
+AU.AA..AU
+ 280  260  150  200 
+ 230  220  110  200 
+ 170  160   50  200 
+ 200  200  200  200 
+AU.AC..AU
+ 280  260  150  200 
+ 340  260  250  200 
+ 200  200  200  200 
+ 340  260  250  200 
+AU.AG..AU
+ 170  160   50  200 
+ 200  200  200  200 
+ 210  200   90  200 
+ 100  -20   50  200 
+AU.AU..AU
+ 200  200  200  200 
+ 310  230  220  200 
+ 220  110  180  200 
+ 290  180  250  200 
+AU.CA..AU
+ 250  310  200  310 
+ 210  200  200  200 
+ 150  240  200  240 
+ 200  200  200  200 
+AU.CC..AU
+ 250  250  200  250 
+ 250  250  200  250 
+ 200  200  200  200 
+ 250  250  200  250 
+AU.CG..AU
+ 150  240  200  240 
+ 200  200  200  200 
+ 190  240  200  240 
+ -30   70  200   70 
+AU.CU..AU
+ 200  200  200  200 
+ 220  220  200  220 
+ 100  190  200  190 
+ 170  160  200  160 
+AU.GA..AU
+ 150  200  210  230 
+ 110  200  160   90 
+  50  200  100  210 
+ 200  200  200  200 
+AU.GC..AU
+ 150  200  210  130 
+ 250  200  270  230 
+ 200  200  200  200 
+ 250  200  270  230 
+AU.GG..AU
+  50  200  100  210 
+ 200  200  200  200 
+  90  200  140  170 
+  50  200   30 -150 
+AU.GU..AU
+ 200  200  200  200 
+ 220  200  240  200 
+ 180  200  150  -20 
+ 250  200  220  230 
+AU.UA..AU
+ 200  310  130  270 
+ 200  200  -10  120 
+ 200  240  110  240 
+ 200  200  200  200 
+AU.UC..AU
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+ 200  240  110  240 
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+AU.UU..AU
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+ 200  160  130   80 
+AU.AA..CG
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+  10    0 -110  200 
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+ 200  200  200  200 
+ 150   70   70  200 
+AU.AG..CG
+  70   60  -50  200 
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+   0 -120  -50  200 
+AU.AU..CG
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+AU.CC..CG
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+ 160  160  200  160 
+ 200  200  200  200 
+  60   60  200   60 
+AU.CG..CG
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+ 150  210  200  210 
+-130  -30  200  -30 
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+-110  200  -60   50 
+ 200  200  200  200 
+AU.GC..CG
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+ 160  200  180  140 
+ 200  200  200  200 
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+ 130  220  200  220 
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+ 180  240  200  240 
+  10  100  200  100 
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+ 140  200  190  120 
+ 220  200  240  200 
+ 200  200  200  200 
+ 220  200  240  200 
+AU.GG..UA
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+ 200  200  200  200 
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+  90  200   70 -110 
+AU.GU..UA
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+ 190  200  160  -10 
+ 220  200  200  200 
+AU.UA..UA
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+ 200  220   10  140 
+ 200  220   90  220 
+ 200  200  200  200 
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+ 200  200  200  200 
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+AU.UU..UA
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+ 200  140  110   60 
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+ 200  200  200  200 
+AU.AC..GU
+ 280  260  150  200 
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+ 200  200  200  200 
+ 340  260  250  200 
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+ 170  160   50  200 
+ 200  200  200  200 
+ 210  200   90  200 
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+AU.AU..GU
+ 200  200  200  200 
+ 310  230  220  200 
+ 220  110  180  200 
+ 290  180  250  200 
+AU.CA..GU
+ 250  310  200  310 
+ 210  200  200  200 
+ 150  240  200  240 
+ 200  200  200  200 
+AU.CC..GU
+ 250  250  200  250 
+ 250  250  200  250 
+ 200  200  200  200 
+ 250  250  200  250 
+AU.CG..GU
+ 150  240  200  240 
+ 200  200  200  200 
+ 190  240  200  240 
+ -30   70  200   70 
+AU.CU..GU
+ 200  200  200  200 
+ 220  220  200  220 
+ 100  190  200  190 
+ 170  160  200  160 
+AU.GA..GU
+ 150  200  210  230 
+ 110  200  160   90 
+  50  200  100  210 
+ 200  200  200  200 
+AU.GC..GU
+ 150  200  210  130 
+ 250  200  270  230 
+ 200  200  200  200 
+ 250  200  270  230 
+AU.GG..GU
+  50  200  100  210 
+ 200  200  200  200 
+  90  200  140  170 
+  50  200   30 -150 
+AU.GU..GU
+ 200  200  200  200 
+ 220  200  240  200 
+ 180  200  150  -20 
+ 250  200  220  230 
+AU.UA..GU
+ 200  310  130  270 
+ 200  200  -10  120 
+ 200  240  110  240 
+ 200  200  200  200 
+AU.UC..GU
+ 200  250   30  170 
+ 200  250  130  170 
+ 200  200  200  200 
+ 200  250  130  170 
+AU.UG..GU
+ 200  240  110  240 
+ 200  200  200  200 
+ 200  240   70  200 
+ 200   70 -250   70 
+AU.UU..GU
+ 200  200  200  200 
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+ 200  190 -120  190 
+ 200  160  130   80 
+AU.AA..UG
+ 280  260  150  200 
+ 250  240  130  200 
+ 150  140   30  200 
+ 200  200  200  200 
+AU.AC..UG
+ 260  250  140  200 
+ 310  230  220  200 
+ 200  200  200  200 
+ 310  230  220  200 
+AU.AG..UG
+ 150  140   30  200 
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+ 210  190   80  200 
+ 130   20   90  200 
+AU.AU..UG
+ 200  200  200  200 
+ 310  230  220  200 
+ 230  120  190  200 
+ 270  150  220  200 
+AU.CA..UG
+ 250  310  200  310 
+ 230  220  200  220 
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+ 480  480  480  480 
+ 330  270  480  300 
+AU.G..CG
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+AU.U..CG
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+AU.A..GC
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+AU.C..GC
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+AU.G..GC
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+AU.U..GC
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+AU.A..UA
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+AU.C..UA
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+AU.G..UA
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+AU.U..UA
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+AU.A..GU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+AU.C..GU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+AU.G..GU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+AU.U..GU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+AU.A..UG
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+AU.C..UG
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+AU.G..UG
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+AU.U..UG
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+CG.A..AU
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+CG.C..AU
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+CG.G..AU
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+CG.U..AU
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+CG.A..CG
+ 230  220  110  400 
+ 210  170  160  400 
+  80   60   40  400 
+ 400  400  400  400 
+CG.C..CG
+ 230  220  400  220 
+ 220  250  400  220 
+ 400  400  400  400 
+ 250  190  400  220 
+CG.G..CG
+ 170  400   80  400 
+ 400  400  400  400 
+  80  400  220  400 
+ 400  400  400  400 
+CG.U..CG
+ 400  400  400  400 
+ 400  220  400  150 
+ 400  400  400  400 
+ 400  170  400  120 
+CG.A..GC
+ 240  220  160  400 
+ 210  170  160  400 
+ 100   60   40  400 
+ 400  400  400  400 
+CG.C..GC
+ 230  220  400  220 
+ 220  250  400  220 
+ 400  400  400  400 
+ 250  190  400  220 
+CG.G..GC
+ 170  400   80  400 
+ 400  400  400  400 
+  80  400  220  400 
+ 400  400  400  400 
+CG.U..GC
+ 400  400  400  400 
+ 400  220  400  130 
+ 400  400  400  400 
+ 400  170  400  120 
+CG.A..UA
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+CG.C..UA
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+CG.G..UA
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+CG.U..UA
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+CG.A..GU
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+CG.C..GU
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+CG.G..GU
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+CG.U..GU
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+CG.A..UG
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+CG.C..UG
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+CG.G..UG
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+CG.U..UG
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+GC.A..AU
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+GC.C..AU
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+GC.G..AU
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+GC.U..AU
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+GC.A..CG
+ 240  220  160  400 
+ 210  170  160  400 
+ 100   60   40  400 
+ 400  400  400  400 
+GC.C..CG
+ 230  220  400  220 
+ 220  250  400  220 
+ 400  400  400  400 
+ 250  190  400  220 
+GC.G..CG
+ 170  400   80  400 
+ 400  400  400  400 
+  80  400  220  400 
+ 400  400  400  400 
+GC.U..CG
+ 400  400  400  400 
+ 400  220  400  130 
+ 400  400  400  400 
+ 400  170  400  120 
+GC.A..GC
+ 250  220  210  400 
+ 210  170  160  400 
+ 120   60   40  400 
+ 400  400  400  400 
+GC.C..GC
+ 230  220  400  220 
+ 220  250  400  220 
+ 400  400  400  400 
+ 250  190  400  220 
+GC.G..GC
+ 170  400   80  400 
+ 400  400  400  400 
+  80  400  220  400 
+ 400  400  400  400 
+GC.U..GC
+ 400  400  400  400 
+ 400  220  400  120 
+ 400  400  400  400 
+ 400  170  400  120 
+GC.A..UA
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+GC.C..UA
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+GC.G..UA
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+GC.U..UA
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+GC.A..GU
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+GC.C..GU
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+GC.G..GU
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+GC.U..GU
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+GC.A..UG
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+GC.C..UG
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+GC.G..UG
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+GC.U..UG
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+UA.A..AU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UA.C..AU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UA.G..AU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UA.U..AU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UA.A..CG
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+UA.C..CG
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+UA.G..CG
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+UA.U..CG
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+UA.A..GC
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+UA.C..GC
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+UA.G..GC
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+UA.U..GC
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+UA.A..UA
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UA.C..UA
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UA.G..UA
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UA.U..UA
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UA.A..GU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UA.C..GU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UA.G..GU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UA.U..GU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UA.A..UG
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UA.C..UG
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UA.G..UG
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UA.U..UG
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+GU.A..AU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+GU.C..AU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+GU.G..AU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+GU.U..AU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+GU.A..CG
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+GU.C..CG
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+GU.G..CG
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+GU.U..CG
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+GU.A..GC
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+GU.C..GC
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+GU.G..GC
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+GU.U..GC
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+GU.A..UA
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+GU.C..UA
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+GU.G..UA
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+GU.U..UA
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+GU.A..GU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+GU.C..GU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+GU.G..GU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+GU.U..GU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+GU.A..UG
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+GU.C..UG
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+GU.G..UG
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+GU.U..UG
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UG.A..AU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UG.C..AU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UG.G..AU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UG.U..AU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UG.A..CG
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+UG.C..CG
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+UG.G..CG
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+UG.U..CG
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+UG.A..GC
+ 320  300  240  480 
+ 290  250  240  480 
+ 180  140  120  480 
+ 480  480  480  480 
+UG.C..GC
+ 310  300  480  300 
+ 300  330  480  300 
+ 480  480  480  480 
+ 330  270  480  300 
+UG.G..GC
+ 250  480  160  480 
+ 480  480  480  480 
+ 160  480  300  480 
+ 480  480  480  480 
+UG.U..GC
+ 480  480  480  480 
+ 480  300  480  210 
+ 480  480  480  480 
+ 480  250  480  200 
+UG.A..UA
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UG.C..UA
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UG.G..UA
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UG.U..UA
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UG.A..GU
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UG.C..GU
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UG.G..GU
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UG.U..GU
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+UG.A..UG
+ 390  370  310  550 
+ 360  320  310  550 
+ 250  210  190  550 
+ 550  550  550  550 
+UG.C..UG
+ 380  370  550  370 
+ 370  400  550  370 
+ 550  550  550  550 
+ 400  340  550  370 
+UG.G..UG
+ 320  550  230  550 
+ 550  550  550  550 
+ 230  550  370  550 
+ 550  550  550  550 
+UG.U..UG
+ 550  550  550  550 
+ 550  370  550  280 
+ 550  550  550  550 
+ 550  320  550  270 
+>POLYC - Penalty for poly C hairpins.
+>First number is penalty for polyC triloop
+>Second number is "slope", i.e. penalty per C in a non triloop
+>Third number is "intercept", i.e. constant penalty for non triloops
+ 140   30  160
+>BETA - Pseudoknot energy parameters.  B1 B2 B3 B1M B1P
+>B1 = Constant penalty for "open" pseudoknot
+>B2 = penalty per pair in pseudoknot
+>B3 = penalty per base in pseudoknot
+>B1M = constant penalty for pseudoknot in a "closed" loop
+>B1P = constant penalty for pseudoknot in a pseudoknot.
+ 960   10   10 1500 1500
+>BIMOLECULAR //TINOCO, 277
+ 409

+#!/usr/bin/python3
+
+from sys import argv
+import subprocess
+import inspect
+from multiprocessing import Pool, TimeoutError, cpu_count
+from os import path, makedirs, getcwd, chdir, devnull
+
+# Retrieve Jar3D Paths from file EditMe
+jar3dexec = ""
+HLmotifDir = ""
+ILmotifDir = ""
+exec(compile(open(path.dirname(path.abspath(inspect.getfile(inspect.currentframe())))+"/EditMe").read(),'','exec'))
+
+class Loop:
+    def __init__(self, header, subsequence, looptype, position):
+        self.header = header
+        self.seq = subsequence
+        self.type = looptype
+        self.position = position
+    def get_header(self):
+        return self.header
+    def subsequence(self):
+        return self.seq
+
+class InsertionSite:
+    def __init__(self, loop, csv_line):
+        # BEWARE : jar3d csv output is crap because of java's locale settings. 
+        # On french OSes, it uses commas to delimit the fields AND as floating point delimiters !!
+        # Parse with caution, and check what the csv output files look like on your system...
+        info = csv_line.split(',') 
+        self.loop = loop                    # the Loop object that has been searched with jar3d
+        self.position = loop.position       # position of the loop's components, so the motif's ones, in the query sequence.
+        self.atlas_id = info[2]             # Motif model identifier of the RNA 3D Motif Atlas
+        self.score = int(float(info[4]))    # alignment score of the subsequence to the motif model
+        self.rotation = int(info[-2])      # should the motif model be inverted to fit the sequence ?
+    def __lt__(self, other):
+        return self.score < other.score
+    def __gt__(self, other):
+        return self.score > other.score
+    
+def enumerate_loops(s):
+    def printLoops(s,loops):
+        print(s)
+        for l in loops:
+            i = 0
+            m=''
+            for c in l:
+                while i<c[0]:
+                    m+=' '
+                    i+=1
+                while i<c[1]+1:
+                    m+='-'
+                    i+=1
+            while i<len(s):
+                m+=' '
+                i+=1
+            print(m,"\tfound in position",l)
+
+    def resort(unclosedLoops):
+        loops.insert(len(loops)-1-unclosedLoops, loops[-1])
+        loops.pop(-1)
+
+    opened = []
+    openingStart = []
+    closingStart = []
+    loops = []
+    loopsUnclosed = 0
+    consecutiveOpenings = []
+    if s[0]=='(': 
+        consecutiveOpenings.append(1)
+    consecutiveClosings = 0
+
+    lastclosed = -1
+    previous = ''
+    for i in range(len(s)):
+
+        # If we arrive on an unpaired segment
+        if s[i] == '.':
+            if previous == '(': 
+                openingStart.append(i-1)
+            if previous == ')': 
+                closingStart.append(i-1)
+
+        # Opening basepair
+        if s[i] == '(':
+            if previous == '(':
+                consecutiveOpenings[-1] += 1
+            else:
+                consecutiveOpenings.append(1)
+            if previous == ')':
+                closingStart.append(i-1)
+                
+            if len(openingStart) and openingStart[-1] == opened[-1]: # We have something like (...(
+                loops.append( [(openingStart[-1],i)] ) # Create a new loop starting with this component.
+                openingStart.pop(-1)
+                loopsUnclosed += 1
+            if len(closingStart) and closingStart[-1] == lastclosed: # We have something like )...( or even )(
+                loops[-1].append( (closingStart[-1],i) ) # Append a component to existing multiloop
+                closingStart.pop(-1)
+
+            opened.append(i)
+
+        # Closing basepair
+        if s[i] == ')':
+            if previous == ')':
+                consecutiveClosings += 1
+            else:
+                consecutiveClosings = 1
+            if previous == '(': # This is not supposed to happen in real data, but whatever.
+                openingStart.append(i-1)
+
+            if len(openingStart) and openingStart[-1] == opened[-1]: # We have something like (...) or ()
+                loops.append( [(openingStart[-1], i)] ) # Create a new loop, and save it as already closed (HL)
+                openingStart.pop(-1)
+                resort(loopsUnclosed)
+            if len(closingStart) and closingStart[-1] == lastclosed: # We have something like )...)
+                loops[-1].append( (closingStart[-1],i) ) # Append a component to existing multiloop and close it.
+                closingStart.pop(-1)
+                loopsUnclosed -= 1
+                resort(loopsUnclosed)
+
+            if i+1<len(s):
+                if s[i+1] != ')': # We are on something like: ).
+                    if consecutiveClosings < consecutiveOpenings[-1]: # an openingStart has not been correctly detected, like in ...((((((...)))...)))
+                        loops.append( [(opened[-2], opened[-1])] ) # Create a new loop (uncompleted)
+                        loopsUnclosed+=1
+
+                    if consecutiveClosings == consecutiveOpenings[-1]: # We just completed an HL+stem, like ...(((...))).., we can forget its info
+                        consecutiveClosings = 0
+                        consecutiveOpenings.pop(-1)
+                    else: # There are still several basepairs to remember, forget only the processed ones, keep the others
+                        consecutiveOpenings[-1] -= consecutiveClosings 
+                        consecutiveClosings = 0
+
+                else: # We are on something like: ))
+                    if consecutiveClosings == consecutiveOpenings[-1]: # we are on an closingStart that cannot be correctly detected, like in ...(((...(((...))))))
+                        loops[-1].append( (i, i+1) ) # Append a component to the uncomplete loop and close it.
+                        loopsUnclosed -= 1
+                        resort(loopsUnclosed)
+                        consecutiveClosings = 0  # Forget the info about the processed stem.
+                        consecutiveOpenings.pop(-1)
+
+            opened.pop(-1)
+            lastclosed = i
+
+        previous = s[i]
+        # print(i,"=",s[i],"\t", "consec. Op=", consecutiveOpenings,"Cl=",consecutiveClosings)
+
+    printLoops(s, loops)
+    return(loops)
+
+def launchJar3d(loop):
+    # write motif to a file
+    newpath = getcwd()+'/'+loop.header[1:] 
+    if not path.exists(newpath):
+        makedirs(newpath)
+    chdir(newpath)
+    filename = loop.header[1:]+".fasta"
+    fasta = open(filename,'w')
+    fasta.write(loop.get_header()+'\n'+loop.subsequence()+'\n')
+    fasta.close()
+
+    # Launch Jar3D on it
+    if loop.type == 'h':
+        cmd = ["java", "-jar", jar3dexec, filename, HLmotifDir+"/all.txt", loop.header[1:]+".HLloop.csv", loop.header[1:]+".HLseq.csv"]
+    else:
+        cmd = ["java", "-jar", jar3dexec, filename, ILmotifDir+"/all.txt", loop.header[1:]+".ILloop.csv", loop.header[1:]+".ILseq.csv"]
+    print(' '.join(cmd))
+    nowhere = open(devnull, 'w')
+    subprocess.call(cmd, stdout=nowhere)
+    nowhere.close()
+
+    # Retrieve results
+    insertion_sites = []
+    if loop.type == 'h':
+        capstype = "HL"
+    else:
+        capstype = "IL"
+    csv = open(loop.header[1:]+".%sseq.csv"%capstype, 'r')
+    l = csv.readline()
+    while l:
+        if "true" in l:
+            insertion_sites.append( InsertionSite(loop, l) )
+        l = csv.readline()
+    csv.close()
+
+    # Cleaning
+    chdir("..")
+    subprocess.call(["rm","-r",loop.header[1:]])
+    return insertion_sites
+
+filename = argv[1]
+basename = filename[0:filename.index('.')]
+
+# Retrieving possible 2D structrures from RNAsubopt
+print("Retrieving possible 2D structures from RNAsubopt...")
+dbn = open(basename+".dbn","w")
+subprocess.call(["RNAsubopt", "-i", filename], stdout=dbn)
+dbn.close()
+dbn = open(basename+".dbn","r")
+dbn.readline()
+s = dbn.readline().split(' ')[0]
+structures = []
+l = dbn.readline()
+while l:
+    structures.append(l.split(' ')[0])
+    l = dbn.readline()
+dbn.close()
+subprocess.call(["rm", basename+".dbn"])
+for ss in structures:
+    print(ss)
+print()
+
+
+# Extracting probable loops from these structures
+print("Extracting probable loops from these structures...")
+HLs = []
+ILs = []
+for ss in structures:
+    loop_candidates = enumerate_loops(ss)
+    for loop_candidate in loop_candidates:
+        if len(loop_candidate) == 1 and loop_candidate not in HLs:
+            HLs.append(loop_candidate)
+        if len(loop_candidate) == 2 and loop_candidate not in ILs:
+            ILs.append(loop_candidate)
+print("TOTAL:")
+print(len(HLs),"probable hairpin loops found")
+print(len(ILs),"probable internal loops")
+print()
+
+# Retrieve subsequences corresponding to the possible loops
+print("Retrieving subsequences corresponding to the possible loops...")
+loops = []
+for i,l in enumerate(HLs):
+    loops.append(Loop(">HL%d"%(i+1), s[l[0][0]-1:l[0][1]], "h", l))
+    print()
+    print(loops[-1].get_header(),"\t\t",l)
+    print(loops[-1].subsequence())
+for i,l in enumerate(ILs):
+    loops.append(Loop(">IL%d"%(i+1), s[l[0][0]-1:l[0][1]]+'*'+s[l[1][0]-1:l[1][1]], "i", l))
+    print()    
+    print(">IL",i+1,"\t\t",l)
+    print(loops[-1].subsequence())
+print()
+
+# Scanning loop subsequences against motif database
+print("Scanning loop subsequences against motif database (using %d threads)..." % (cpu_count()-1))
+pool = Pool(processes=cpu_count()-1)
+insertion_sites = [ x for y in pool.map(launchJar3d, loops) for x in y ]
+insertion_sites.sort(reverse=True)
+print(len(insertion_sites), "insertions found:")
+
+# Writing results to file
+c = 0
+resultsfile = open(basename+".sites.csv","w")
+resultsfile.write("Motif,Rotation,Score,Start1,End1,Start2,End2\n")
+for site in insertion_sites:
+    if site.score > 10:
+        c+=1 
+        string = "FOUND with score %d:\t\t possible insertion of motif "% site.score + site.atlas_id
+        if site.rotation:
+            string += " (reversed)"
+        string += " at positions"
+        print(string, site.loop.subsequence(), '*'.join([str(x) for x in site.position]))
+    resultsfile.write(site.atlas_id+','+str(bool(site.rotation))+",%d"%site.score+',')
+    positions = [','.join([str(y) for y in x]) for x in site.position]
+    if len(positions)==1:
+        positions.append("-,-")
+    resultsfile.write(','.join(positions)+'\n')
+if c< len(insertion_sites):
+    print("... and %d more with score(s) below 10."% (len(insertion_sites)-c))   
+resultsfile.close()

-#ifndef COMPONENT_H
-#define COMPONENT_H
-
-#include <string>
-
-class Component 
-{
-    public:
-        Component();
-        Component(std::string& cons_seq, uint k);
-    private:
-        std::string     _cons_seq;
-        uint            k;
-};
-
-
-istream& operator>>(istream& is, Component& m);
-ostream& operator<<(ostream& os, const Component& m);
-
-#endif
\ No newline at end of file

-#include "Motif.h"
\ No newline at end of file

-#ifndef MOTIF_H
-#define MOTIF_H
-
-#include <vector>
-#include <string>
-#include "Component.h"
-
-class Motif
-{
-    public:
-        Motif();
-        Motif(std::string filename);
-        ~Motif();
-        std::vector<Component>& getComponents() const;
-        Component& getComponent(uint k) const;
-        std::string name;
-
-    private:
-        std::vector<Component>  _comps;
-
-};
-
-istream& operator>>(istream& is, Motif& m);
-ostream& operator<<(ostream& os, const Motif& m);
-
-#endif
\ No newline at end of file

-#include "RNA.h"
-
-RNA::RNA() {}
-
-RNA::~RNA() {}
-
-RNA::RNA(std::string seq) : _seq(seq) { }

-#ifndef RNA_H
-#define RNA_H
-
-#include <string>
-
-class RNA {
-    public:
-        RNA();
-        RNA(std::string);
-        ~RNA();
-        uint            length() const;
-        std::string     str() const;
-        // char            seq(uint k) const;
-        // bool            isConsensus() const;
-        // bool            containsPseudoBases() const;
-    private:
-        std::string     _seq;
-        // bool            _coding;
-        // bool            _consensus;
-        // bool            _containsPseudoNTs;
-};
-
-inline uint RNA::length() const { return _seq.length(); }
-inline std::string RNA::str() const { return _seq; }
-
-#endif
\ No newline at end of file

-#include "Motif.h"
-#include <cstdlib>
-#include <iostream>
-#include <unistd.h>
-#include <boost/program_options.hpp>
-#include <boost/filesystem.hpp>
-
-#include "RNA.h"
-
-using namespace std;
-namespace bpo = boost::program_options;
-namespace bf = boost::filesystem;
-
-bool checkMotifFolder(bf::path & folder)
-{
-    if (not(bf::is_directory(folder) and bf::exists(folder))) return false;
-    bf::directory_iterator end_itr;
-    uint Ndesc = 0;
-    for (bf::directory_iterator itr(folder); itr != end_itr; ++itr)
-    {
-        if (itr->path().leaf().string().find(string(".desc")) != std::string::npos)
-            Ndesc++;
-    }
-    cout << "Found " << Ndesc << " .desc files in " << folder.string() << endl;
-    if (Ndesc > 0)
-        return true;
-    return false;
-}
-
-int parseMotifs(bf::path & folder)
-{
-    bf::directory_iterator end_itr;
-    for (bf::directory_iterator itr(folder); itr != end_itr; ++itr)
-    {
-        if (itr->path().leaf().string().find(string(".desc")) != std::string::npos)
-        {
-            
-        }
-    }
-
-}
-
-int main(int argc, char** argv)
-{
-    bf::path                    currentFolder(bf::current_path());
-    bf::path                    motifFolderPath(currentFolder); // By default, searching here...
-    bpo::options_description    desc("Options"); 
-    bpo::variables_map          options_map;
-    RNA                         querySequence;
-
-    desc.add_options() 
-      ("help", "Print this help message")
-      ("seq,s", bpo::value<string>()->required(), "RNA sequence to find motives in.")
-      ("motifs,m", bpo::value<bf::path>(), "Path to folder of DESC files describing the motifs to be used") 
-    ;
-    bpo::store(bpo::parse_command_line(argc, argv, desc), options_map);
-    bpo::notify(options_map);
-
-    if (options_map.count("help")) { 
-        cout << desc << endl; 
-        return EXIT_SUCCESS; 
-    } 
-    if (options_map.count("motifs")) {
-        motifFolderPath = options_map["motifs"].as<bf::path>();
-        if (not(checkMotifFolder(motifFolderPath))) { return EXIT_FAILURE; }
-    }
-    if (options_map.count("seq")) {
-        querySequence = RNA(options_map["seq"].as<string>());
-    }
-    cout << "Working with sequence " << querySequence.str() << " (length " << querySequence.length() << ")." << endl;
-
-    return EXIT_SUCCESS;
-}