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>
#define rep(i,n) for(int i=0;i<n;++i)
#define rrep(i,n) for(int i=n-1;i>=0;--i)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define yesno(flg) if(flg){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}
#define vi vector<int>
#define pb push_back
#define i197 1000000007
#define MAX_N 200002
using namespace std;

typedef long long ll;
typedef pair<int,int> Pii;
typedef pair<Pii,int> Piii;
typedef pair<int,ll> Pil;
typedef pair<ll,ll> Pll;
typedef pair<string,int> Psi;
typedef pair<Psi,int> Psii;

const int inf=1000000000;
struct edge{
	int myc,to,c,cost;
};
struct pos{
	int to,cost,color;
};
int dy[]={0, 0, 1, -1};
int dx[]={1, -1, 0, 0};

int main() {
	int n,d;
	int s[160];
	rep(i,160)s[i]=i*i;
	cin>>n>>d;
	int x[10][10];
	rep(i,n){
		rep(j,d)cin>>x[i][j];
	}
	int res=0;
	rep(i,n){
		rep(j,n){
			int dis=0;
			rep(k,d){
				dis+=(x[i][k]-x[j][k])*(x[i][k]-x[j][k]);
			}
			bool flg=false;
			rep(k,159){
				if(s[k+1]==dis)flg=true;
			}
			if(flg)res++;
		}
	}
	cout<<res/2<<endl;
	return 0;
}