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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input){
  input = input.split("\n");
  inputStr = input[0].split(" ");
  var N = Number.parseInt(inputStr[0]);
  var D = Number.parseInt(inputStr[1]);
  var X_arr = [];
  var count = 0;
  //引数の配列を数値変換してX_arrに溜め込む。配列は擬似的な二次元配列
  for (var i = 0; i < N ; i++){  
    var tmp = input[i+1].split(" ");
    X_arr.push(tmp.map( tmp => parseInt(tmp)));
  }
  //ループで回しながら計算する
  for(var i1 = 0; i1 < N-1 ; i1++ ){
	//中間変数tmpを定義
    var tmp1 = X_arr[i1].map(tmp => parseInt(tmp));
    
    for(var i2=i1+1; i2 < N ; i2++){
      var cul = 0;
      var tmp2 = X_arr[i2].map(tmp => parseInt(tmp));
      
      //D=配列の横分ループを回して各要素の計算結果を足しこむ。
      for(var i3 = 0 ; i3 < D ; i3++){
        cul = cul + Math.pow(tmp1[i3]-tmp2[i3],2)
      }
      if (Number.isInteger(Math.sqrt(cul))){
        count += 1;
      }
    }
  }
  console.log(count);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));