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>
#include <stdlib.h>

int main(void){
    int D, N, i, j, k, x, y, z, count;
    double result, sum;
    printf("D&N\n");
    char buf[256];
    fgets(buf,256,stdin);
    sscanf(buf, "%d %d", &D, &N);
    if(N > 10|N < 2|D > 10|D < 1){
        return 0;
    }
    int dim[D][N];
    for(i = 0; i < D; i++){
        for(j = 0; j < N; j++){
            char buf[256];
            fgets(buf,256,stdin);
            sscanf(buf, "%d", &dim[i][j]);
            if(dim[i][j] > 20| dim[i][j] < -20){
                return 0;
            }
        }
    }
    
    i = 0;
    j = 0;
    count = 0;
    for(j=0; j<D-1; j++){
        for(k=j+1; k<D; k++){
            sum = 0;
            for(i=0; i<N; i++){
                x = dim[j][i];
                y = dim[k][i];
                z = abs(x - y);
                sum = sum + z * z;
                
            }result = sqrt(sum);
            if(ceil(result) != floor(result)){
            } else{
                count++;
            }
        }
    }
    printf("%d\n", count);
    return 0;
}