using System;
using static System.Math;
public class plainmc{

public static double[] integrate(Func<vector,double> f,vector a, vector b, int N){
        double V=1;
        for(int i=0;i<a.size;i++) V*=(b[i]-a[i]);
        double[] r=sample(f,a,b,N);
        double integ=V*r[0];
        double error=V*r[1]/Sqrt(N);
        return new double[] {integ,error};
        }

public static void randomx(vector x,vector a,vector b,Random[] rnds){
	for(int i=0;i<x.size;i++)x[i]=a[i]+rnds[i].NextDouble()*(b[i]-a[i]);
	}

public static double[] sample(Func<vector,double>f,vector a,vector b,int N){
	int dim=a.size;
	var rnds=new Random[dim]; 
	vector x=new vector(dim);
	double sum=0,sum2=0;
	for(int i=0;i<dim;i++)rnds[i]=new Random();
	for(int i=0;i<N;i++){
		randomx(x,a,b,rnds);
		double fx=f(x);
		sum+=fx;
		sum2+=fx*fx;
		}
	double average=sum/N, variance=sum2/N-average*average;
	return new double[] {average,variance};

}
}//class