#include <iostream>
#include <cmath>
#include <math.h>
#include <vector>
#include "cavlib/constants.hh"
#include "gsl/gsl_rng.h"
using namespace std;

double evaluate_integral (int N)
{
    gsl_rng *rng = gsl_rng_alloc(gsl_rng_default);
    gsl_rng_set(rng, time(NULL));

    const int num_variables = 8;
    std::vector<double> x(num_variables);
    for (int i = 0; i < num_variables; i++)
    {
        x[i] = gsl_rng_unform(rng) * C::pi / 8 ;
    }

    double integral = sin (x[0] + x[1] + x[2] + x[3] + x[4] + x[5] + x[6] + x[7]);
    double integral_sum;
    int j = 0;

    while (j < N)
    {
        j++;
        integral_sum = integral_sum + integral;
    }
    return integral_sum;
}

int main ()
{
    int N;
    cin >> N;
    double final_result;
    final_result = evaluate_integral (N) / N * pow(10,6) * pow(C::pi / 8,8);
    cout << "This integral evaluates to " << final_result;
}