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>
#include<string.h>
using namespace std;
#define FAST ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define Max(x,y,z) max(x,max(y,z))
#define Min(x,y,z) min(x,min(y,z))
#define fr(i,s,e) for(i=s;i<e;i++)
#define rf(i,s,e) for(i=s-1;i>=e;i--)
#define pb push_back
#define eb emblace_back
#define mp make_pair
#define ff first
#define ss second
//#define int   long long
#define ll   long long
#define trace1(x)                cerr<<#x<<": "<<x<<endl
#define trace2(x, y)             cerr<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x, y, z)          cerr<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a, b, c, d)       cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define trace5(a, b, c, d, e)    cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<endl
#define trace6(a, b, c, d, e, f) cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<<f<<endl
#define vl vector<long long>
#define inf (1LL<<61)
#define vi vector<int>
#define vii vector< vector<int> >
#define vll vector< vector<long long> >
#define vpi vector< pair<int,int> >
#define vpl vector< pair<ll,ll> >
#define viii vector< vector<vector<int> > >
typedef pair<pair<int, int>,int> P;
#define cd complex<double>
#define PI 4*atan(1)
#define mod %1000000007
#define pi 3.14159265358979323846//20 decimals
#define ld long double

int main()
{
	FAST;
	ll n, d, i, j, k;
	cin >> n >> d;
	ld x[n][d];
	fr(i,0,n)
		fr(j,0,d)
			cin >> x[i][j];
	ll ans = 0;
	fr(i,0,n)
		fr(j, i+1, n)
		{
			ld dis = 0;
			fr(k,0,d)
				dis = dis + (x[i][k] - x[j][k])*(x[i][k] - x[j][k]);
			dis = sqrt(dis);
			if((dis - (ll)dis) < 0.0000001)
				ans++;
		}
	cout << ans;
}