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: Runtime Error)

function Main(input) {
  const input = input.split("\n");
  const args0 = input[0].split(" ");
  const num = parseInt(args0[0], 10);
  const dim = parseInt(args0[1], 10);
  var count = 0;
  var vector = new Array;
  for(var i = 1; i < num; i++){
    var spot = input[i].split(“ “);
    for(var j = 0; j < spot.length; j++){
      spot[j] = parseInt(spot[j]);
    }
    vector.push(spot);
    for(var k = 1; k < j; k++){
      var rspot = vector[k-1];
      var rdis = 0;
      for(var l = 0; l < dim; l++){
        rdis = rdis + (rspot[l] - spot[l]) * (rspot[l] - spot[l]);
      }
      var dis = Math.sqrt(rdis);
      if(Number.isInteger(dis)){
        count++;
      }
    }
  }
  console.log(feeTaxi);
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));