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)

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()
typedef long long ll;
// #include<C:\Users\J\Desktop\AC\athead.h>
#define showa(v) for(int iii = 0; iii < v.size(); iii++){ cout << v[iii] << " ";} cout << endl;
#define show(iiii) cout << iiii << endl; 
#define shows(iiiii) cout << iiiii << " ";
#include<iostream>
#include<string>
#include<vector>
#include<stdio.h>
#include <cmath>
#include <cstdlib>
#include <cassert>
#include <algorithm>
#include <set>
#include <deque>
#include <numeric>
#include<tuple>
#include <utility>
#include <map>
#define waru 1000000000+7

using namespace std;

bool che(vector<int> y,vector<int> z){
  int sum = 0;
  rep(i, y.size()){
    sum += (y[i] - z[i])*(y[i] - z[i]);
  }
  int root = sqrt(sum);
  return root*root == sum;
}

int main(){
  int n, d;
  cin >> n >> d;
  vector<vector<int>> x;
  rep(i,n){
    vector<int> buf(d);
    rep(j,d){
      cin >> buf[j];
    }
    x.push_back(buf);
  }
  int res = 0;
  for(int i = 0; i < n; i++){
    for(int j = i+1; j < n; j++){
      if(che(x[i], x[j])){
        res++;
      }
    }
  }
  cout << res;


}