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>


int D,N,n,d,x[100][100],q[110];
int uke(int x[100][100])
{
	scanf("%d%d",&N,&D);
	for(n=1;n<=N;n++){
		for(d=1;d<=D;d++){
			scanf("%d",&x[n][d]);
		}		
	}
	return x[n][d];
}
int y[30],p[30];
int sa(int y[30])
{	
	for(d=1;d<=D;d++){
		for(n=1;n<=N;n++){
			if (n == d) continue;
				q[n] = 0;
			for (int k = 0; k < d; k++) {
				q[n] += (x[n][k] - x[d][k]) * (x[n][k] - x[d][k]);
			}		
			
			
		}	
			/*y[d]=x[n][d]-x[n+1][d];
			
			p[d]=y[d]*y[d];
			q[n]=p[n]+p[n+1];
		}	
		y[d]=x[1][d]-x[N][d];
		p[d]=y[d]*y[d];
		q[n]=p[n]+p[n+1];*/
	
	}

	for(int x=0;x<20;x++){		
		if(q[n]==x*x){
			return 1;
		}
	}
}



int num=0;

int main()
{
	uke(x);
	sa(y);
	if(sa(y)){
		num++;
	}
	printf("%d\n",num);
	return 0;
}