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<iostream>
#include<vector>
#include<cmath>
using namespace std;
int main() {
  int n,d,ans=0;
  cin >> n >> d;
  vector<vector<int>> X(n,vector<int>(d)); // vector<vector<int>> X[n]; として,dで回して見かけ上二次元配列にしてもよい.
  for(int i=0;i<n;i++){
    for(int j=0;j<d;j++){
      cin >> X[i][j];
    }
  }
  // 全てのiとjについての探索 O(n*n*d)
  for(int i=0;i<n;i++){
    for(int j=i+1;j<n;j++){
      int ddist=0; // 2点間の距離の二乗
      for(int k=0;k<d;k++){
        int dist = abs(X[i][k]-X[j][k]); // 2点間の距離
        ddist += dist*dist;
      }
      // ddistが平方数であるかどうかの判定
      bool flag = false;
      for(int k=0;k*k<=ddist;k++){
        if(k*k==ddist) flag = true;
      }
      if(flag) ans++;
    }
  }
  cout << ans << endl;
  return 0;
}