#include <iostream>
#include <cmath>

using namespace std;

const int SIZE = 10;

int
main()
{
    float x[SIZE];
    float y[SIZE];
    float sum_x2 = 0, sum_y2 = 0;
    float lengthx, lengthy;
    int i, n;

    // See how many elements we have
    cout << "How many elements in x and y?" << endl;
    cin >> n;

    // Check we have room for them
    if (n > SIZE) {
	cout << "We don't have room for that many" << endl;
	return (0);
    }

    // Read in x
    cout << "Enter the elements of x:" << endl;
    for (i = 0; i < n; i++) {
	cin >> x[i];
    }

    // Read in y
    cout << "Enter the elements of y:" << endl;
    for (i = 0; i < n; i++) {
	cin >> y[i];
    }

    // Sum the square of each element in x and y
    for (i = 0; i < n; i++) {
	sum_x2 += x[i] * x[i];
	sum_y2 += y[i] * y[i];
    }

    // The length is the square root of the sum of the squares
    lengthx = sqrt(sum_x2);
    lengthy = sqrt(sum_y2);

    // Print out the lengths
    cout << "Length x: " << lengthx << endl;
    cout << "Length y: " << lengthy << endl;

    // Divide each element by the length of its vector
    for (i = 0; i < n; i++) {
	x[i] /= lengthx;
	y[i] /= lengthy;
    }

    // Reset sums
    sum_x2 = sum_y2 = 0;

    // Recompute the sum of the squares
    for (i = 0; i < n; i++) {
	sum_x2 += x[i] * x[i];
	sum_y2 += y[i] * y[i];
    }

    // Recompute the lengths
    lengthx = sqrt(sum_x2);
    lengthy = sqrt(sum_y2);

    // Printf out the lengths (they should both be 1)
    cout << "Length x: " << lengthx << endl;
    cout << "Length y: " << lengthy << endl;

    return (0);
}