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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
const int square[] = {0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961,1024,1089,1156,1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,2401,2500,2601,2704,2809,2916,3025,3136,3249,3364,3481,3600,3721,3844,3969,4096,4225,4356,4489,4624,4761,4900,5041,5184,5329,5476,5625,5776,5929,6084,6241,6400,6561,6724,6889,7056,7225,7396,7569,7744,7921,8100,8281,8464,8649,8836,9025,9216,9409,9604,9801,10000,10201,10404,10609,10816,11025,11236,11449,11664,11881,12100,12321,12544,12769,12996,13225,13456,13689,13924,14161,14400,14641,14884,15129,15376,15625,15876,16129};

int compare_int(const void *a, const void *b){
    return *(int*)a - *(int*)b;
}

int n, a, i, j;
int d, k;
int z;
int x[10][10];
void *f;

int main(void){
	scanf("%d%d", &n, &d);
	for(i=0; i<n; i++){
		for(k=0; k<d; k++){
			scanf("%d", &x[i][k]);
		}
	}
	for(i=0; i<n; i++){
		for(j=i+1; j<n; j++){
			z=0;
			for(k=0; k<d; k++){
				z += (x[i][k]-x[j][k])*(x[i][k]-x[j][k]);
			}
			f=bsearch(&z, square, sizeof(square), sizeof(int), compare_int);
			if(f!=NULL){a++;}
		}
	}
	printf("%d\n", a);
}