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 "bits/stdc++.h"
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define REPR(i, n) for(int i = n; i >= 0; i--)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size)
#define MOD 1000000007
const long long mod = 1e9+7;
typedef vector<long long> Vl;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<Vl> VVl;
typedef pair<int, int> PII;
typedef long long ll;

int main(){
    int a=0,b=0,d=0,n=0,y=0;
    double c=0;
    string s,s1,s2;
    cin >> n >> d;
    VVI x(n,vector<int>(d,0));

    rep(i,n){
        rep(j,d){
            cin >>x[i][j];
        }
    }

    for (int i=0;i<n-1;i++){
        for (int j=i+1;j<n;j++){
            for (int k=0;k<d;k++){
                c += abs(x[i][k] - x[j][k]) * abs(x[i][k] - x[j][k]);
            }
            c = sqrt(c);
            if (ceil(c) == floor(c)){
                y++;
            }
            c=0;
        }
    }

    cout << y <<endl;

    return 0;
}