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: Accepted)

/*
	submission # - User: herp_sy
	https://atcoder.jp/contests/
*/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdbool.h>

#define _CRT_SECURE_NO_WARNINGS
#define TLong long long
#define TBMod 1000000007

// fact(n)
int fact(int n){
	if(n == 1)	return 1;
	else return (n * fact(n - 1));
}

// nCr(n,r)
int nCr(int n, int r){
	if(r == 0 || r == n)	return 1;
	else if(r == 1)	return n;
	return (nCr(n - 1, r - 1) + nCr(n - 1, r));
}

// gcd(a,b)
int gcd(int a,int b){
	if(a == 0) return b;
	else if(b == 0) return a;
	else return gcd(b,a % b);
}

// lcm(a,b)
int lcm(int a,int b){
	return (a * b) / gcd(a,b);
}

// swap(&a, &b);
void swap(int *a,int *b){
	int tmp;
	tmp = *a;	*a = *b;	*b = tmp;
	return;
}

// qsort(array, size, sizeof(int),comp);
int ASC(const int *a,const int *b){
	return (*a - *b);
}

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

// append(array,*size,addNum)
void append(int *array,int *size,int num){
	realloc(array, sizeof(int) * (*size + 1));
	array[(*size)] = num;
	++(*size);
}

// pop(array,*size) & nongetpop(array,*size)
int pop(int *array,int *size){
	int temp = array[(*size - 1)];
	nongetpop(array,&(*size));
	return temp;
}

int nongetpop(int *array,int *size){
	realloc(array,sizeof(int) * (*size - 1));
	--(*size);
}

int main(int argc, char const *argv[])
{
	int n,d;
	int x[13][13];
	int dis,temp;
	int cnt = 0;
	scanf("%d%d",&n,&d);
	for (int i = 0; i < n; ++i)
	{
		for (int j = 0; j < d; ++j)	scanf("%d",&x[i][j]);
	}
	for (int i = 0; i < n; ++i)
	{
		for (int j = i + 1; j < n; ++j)
		{
			dis = 0;
			for (int k = 0; k < d; ++k)
			{
				temp = abs(x[i][k] - x[j][k]);
				dis += (temp * temp);
			}
			if( (int)sqrt((double)dis) * (int)sqrt((double)dis) == dis ){
				++cnt;
			} 
		}
	}
	printf("%d\n", cnt);
	return 0;
}