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 ff first
#define ss second
#define pb push_back
#define mp make_pair
#define endl "\n"
#define ll long long
#define ld long double
#define l_b lower_bound
#define u_b upper_bound
#define vi vector<int>
#define vll vector<ll>
#define pii pair<int,int>
#define pll pair<ll, ll>
#define vpii vector<pii>
#define vpll vector<pll>
#define heap priority_queue
#define umap unordered_map
#define sz(a) int((a).size())
#define all(c) c.begin(),c.end()
#define test() ll t;cin>>t;while(t--)
#define mset(a,x) memset(a,x,sizeof(a))
#define rep(i,a,n) for(ll i = a; i < n; ++i) 
#define debug(x) cout<<(#x)<<" is "<<(x)<<endl
#define fastIO ios_base::sync_with_stdio(0);cin.tie(0)
 
const int inf = 1e9;
const int mod = 1e9 + 7;
const int N = 1e6 + 5;

int pt[20][20];

int check(float val){
	int x = sqrt(val);
	return (x*x == val);
}

int main() {
	// fastIO;
    int n, d;
    cin >> n >> d;
    rep(i, 0, n)
    	rep(j, 0, d)
    		cin >> pt[i][j];
    int ans = 0;
    rep(i, 0, n){
    	rep(j, i+1, n){
    		float dis = 0;
	    	rep(k, 0, d){
	    		dis += (pt[j][k]-pt[i][k])*(pt[j][k]-pt[i][k]);	
	    	}
	    	if(check(dis))
	    		ans++;
	    }
    }
    cout << ans;

	return 0;
}