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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>

int main(void)
{
  //dとnを入力
  int d,n;
  scanf("%d%d",&d,&n);

  //n個の座標をforで入力
  int i,j,k;
  int x[n][d];
  for(i=0;i<n;i++)
    for(k=0;k<d;k++)
      scanf("%d",&x[i][k]);

  //計算開始
  float dist;
  int cnt=0;
  //i,jを決める
  for(i=0;i<n;i++)
    for(j=i+1;j<n-i;j++){

      //点iと点jの距離を求める
      dist = 0;
      for(k=0;k<d;k++)
        dist += (x[i][k]-x[j][k])^2;
      dist = sqrt(dist);

      //ceil(切り上げ関数)とfloor(切り捨て関数)を使ってdistが整数か判定
      //distが整数ならcntを1増やす
      if(ceil(dist)!=floor(dist))
        cnt++;
    }

  //cntを出力して終了
  printf("%d\n",cnt);
  return 0;
}