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)

/*                        ______
 _______   /\     |``\   |        |  /
    |     /  \    |__/   |____    |/
    |    / _ _\   |  \   |        |\
    |   /      \  |   \  |______  |  \

            Dept. of CSE
        Comilla  University

*/
#include<bits/stdc++.h>
#define pi 2*acos(0.0)
#define ll long long
#define FIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define Node struct node
#define spc " "
#define  E  2.71828182845904523536
#define pb push_back
#define pp pop_back
#define valid(nx,ny) nx>=0 && nx<n && ny>=0 && ny<m
#define ee endl
#define pii pair<int,int>
#define infinity 10000000000000000
#define mod 1000000007
int fx[]={0,0,+1,-1};
int fy[]={+1,-1,0,0};

using namespace std;
///check n=1;
///check corner case;
const int maX=1e5+1;
vector<ll>Graph[maX],cost[maX];
ll visit[maX];
ll x[10];
ll y[10];

int main()
{
    ll n,d,i,j,cc=0;
    cin>>n>>d;
    vector<ll>ara[n];
    for(i=0;i<n;i++){
        for(j=0;j<d;j++){
            ll x;cin>>x;
            ara[i].pb(x);
        }
    }
    for(i=0;i<n-1;i++){
        for(ll k=i+1;k<n;k++){
            ll x=0;
            for(j=0;j<d;j++){
                 x+=abs(ara[i][j]-ara[k][j])*abs(ara[i][j]-ara[k][j]);
            }
            ll y=sqrt(x);
            if(y*y==x)cc++;
        }

    }
    cout<<cc<<endl;
return 0;
}