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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(){
  
  int d,n,c=0,count=0;
  scanf("%d %d",&n,&d);
while(c==0){
    if(2<=n&&n<=10&&1<=d&&d<=10){
      c++;
    }
    scanf("%d %d",&n,&d);
  }
  int data[n][d];
  for(int i=0;i<n;i++){
    for(int j=0;j<d;j++){
      scanf("%d",&data[i][j]);
    }
  }
  
  int count2=0;
  double xs=1.0;
  for(int i=0;i<n;i++){
    double sum=0.0;
    
    if(i==n-1){
      sum+=pow(abs(data[i][count]-data[0][0]),2.0)+pow(abs(data[0][1]-data[i+1][count+1]),2.0);
    }else{
    sum+=pow(abs(data[i][count]-data[i+1][count]),2.0)+pow(abs(data[i][count+1]-data[i+1][count+1]),2.0);
    }
    if(fmod(sum,xs)==0.0){
      count2++;
    }
    count++;	
  } 
  printf("%d",count2);
  
}