#include <iostream>
#include <cmath>
#include <vector>

using namespace std;


vector<vector<double>> romber(double (*function)(double), double a, double b, int M){
    double h = b - a;
    vector<vector<double>> R;
    R.push_back({});
    double first_value = h * (function(a) + function(b)) / 2.0;
    R[0].push_back(first_value);
    for (int n = 0; n < M; n++){
        h = h / 2.0;
        double inner_sum = 0;
        for (int i = 1; i < pow(2, n-1); i++){
            inner_sum += function(a + (2*i - 1) * h);
        }
        double column_value = 1.0 / 2.0 * R[n][0] + h * inner_sum;
        inner_sum = 0;
        R.push_back({});
        R[n+1].push_back(column_value);
        for(int m = 0; m < n; m++){
            double row_value = R[n+1][m] + (R[n+1][m]-R[n][m]) / (pow(4, m) - 1);
            R[n+1].push_back(row_value);
        }
    }
    //print
    for (int i = 0; R.size(); i++){
        for(int j = 0; R[i].size(); j++){
            cout << R[i][j] << ' ';
        }
        cout << endl;
    }
    return R;
}


int main(){
    vector<vector<double>> result;
    romber(&sin, 0, M_PI, 4);
    cout << result.size() << endl;
    cout << result[1].size() << endl;

    return 0;
}