Problem:
Score : 200 points

Problem Statement

There are N points in a D-dimensional space.

The coordinates of the i-th point are (X_{i1}, X_{i2}, ..., X_{iD}).

The distance between two points with coordinates (y_1, y_2, ..., y_D) and (z_1, z_2, ..., z_D) is \sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + ... + (y_D - z_D)^2}.

How many pairs (i, j) (i < j) are there such that the distance between the i-th point and the j-th point is an integer?

Constraints

All values in input are integers.

2 \leq N \leq 10

1 \leq D \leq 10

-20 \leq X_{ij} \leq 20

No two given points have the same coordinates. That is, if i \neq j, there exists k such that X_{ik} \neq X_{jk}.

Input

Input is given from Standard Input in the following format:

N D
X_{11} X_{12} ... X_{1D}
X_{21} X_{22} ... X_{2D}
\vdots
X_{N1} X_{N2} ... X_{ND}

Output

Print the number of pairs (i, j) (i < j) such that the distance between the i-th point and the j-th point is an integer.

Sample Input 1

3 2
1 2
5 5
-2 8

Sample Output 1

1

The number of pairs with an integer distance is one, as follows:

The distance between the first point and the second point is \sqrt{|1-5|^2 + |2-5|^2} = 5, which is an integer.

The distance between the second point and the third point is \sqrt{|5-(-2)|^2 + |5-8|^2} = \sqrt{58}, which is not an integer.

The distance between the third point and the first point is \sqrt{|-2-1|^2+|8-2|^2} = 3\sqrt{5}, which is not an integer.

Sample Input 2

3 4
-3 7 8 2
-12 1 10 2
-2 8 9 3

Sample Output 2

2

Sample Input 3

5 1
1
2
3
4
5

Sample Output 3

10

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <vector>
#include <cmath>
#include <tuple>
#include <cmath>
#include <algorithm>
#include <map>
#include <iomanip>
#include <queue>
#include <numeric>
#include <iostream>
#include <set>

using namespace std;

bool isValid(vector<int> xs, vector<int> ys, int n) {

    int d = 0;

    for (int i = 0; i < n; i++) {

        d += (xs[i] - ys[i]) * (xs[i] - ys[i]);

    }

    bool ok = false;

    for (int i = 1; i <= d; i++) {

        if (i * i == d) {
            ok = true;
        }

    }

    return ok;

}


int main() {

    int N, D;
    cin >> N >> D;

    vector<vector<int>> vs;

    for (int i = 0; i < N; i++) {
        vector<int> v;
        for (int j = 0; j < D; j++) {
            int x;
            cin >> x;
            v.push_back(x);
        }
        vs.push_back(v);
    }

    int result = 0;

    for (int i = 0; i < N; i++) {
        for (int j = i + 1; j < N; j++) {


            if (isValid(vs[i], vs[j], D)) {
                result += 1;
            }

        }
    }

    cout << result << "\n";

    return 0;
}