#include<iostream>

using namespace std;

int main(){
    int n;
    cout << "Input highest grade: "; cin >> n;
    double x[n], y[n], y1[n], y2[n], y3[n], N=0, xp;

    for (int i=0; i<=n; i++){
    	cout << "Input x[" << i << "] :"; cin >> x[i];
    }

    cout << endl;

    for (int i=0; i<=n; i++){
    	cout << "Input y[" << i << "] :"; cin >> y[i];
    }

    cout << endl;

    for (int i=0; i<n; i++){
    	y1[i] = (y[i+1] - y[i]) / (x[i+1] - x[i]);
    	cout << "y1[" << i << "] (" << i << ", " << i+1 << ") = " << y1[i] << endl;
	}

    cout << endl;

  	for (int i=0; i<n-1; i++){
    	y2[i] = (y1[i+1] - y1[i]) / (x[i+2] - x[i]);
    	cout << "y2[" << i << "] (" << i << ", " << i+1 << ", " << i+2 << ") =" << y2[i] << endl;
    }

    cout << endl;

    for (int i=0; i<n-2; i++){
    	y3[i] = (y2[i+1] - y2[i]) / (x[i+3] - x[i]);
		cout << "y3[" << i << "] (" << i << ", " << i+1 << ", " << i+2 << ", " << i+3 << ") =" << y3[i] << endl;
    }

    cout << "Input x for N(x): "; cin >> xp;
    cout << "N(" << n << ") {" << xp << "}= " << y[0] + (y1[0] * (xp-x[0])) + (y2[0] * (xp-x[0]) * (xp-x[1])) + (y3[0] * (xp-x[0]) * (xp-x[1]) * (xp-x[2]));

  	return 0;
}