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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define rep(i,a,b) for(ll i=a;i<b;i++)
#define repv(i,a,b) for(ll i=b-1;i>=a;i--)
#define MAXN 300005
#define endl "\n"

ll gcd(ll a,ll b){if(b==0) return a; else return gcd(b,a%b);}
ll power(ll x,ll y){ll res=1; while(y>0){if(y&1) res=res*x;y=y>>1;x=x*x;}return res;}

int n,d,arr[15][15];

int main()
{
	ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin>>n>>d;
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=d;j++) cin>>arr[i][j];
    }
    int cnt=0;
    for(int i=1;i<n;i++)
    {
        for(int j=i+1;j<=n;j++)
        {
            int sum=0;
            for(int k=1;k<=d;k++)
            {
                sum+=((arr[j][k]-arr[i][k])*(arr[j][k]-arr[i][k]));
            }
            int p=sqrt(sum);
            if(p*p==sum) cnt++;
        }
    }
    cout<<cnt<<endl;
}