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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int INF = 1e9;
const ll LINF = 1e18;
const int mod = 1e9+7;

#define pi pair<int,int>
#define pl pair<lld,lld>

#define dump(x) cout << #x << " = " << (x) << endl
#define YES(n) cout << ((n) ? "YES" : "NO"  ) << endl
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
#define SANKOU(n,a,b) cout << ((n) ? (#a) : (#b) ) << endl

#define mem0(x) memset(x,0,sizeof(x))
#define fillnum(x,n) fill(begin(x),end(x),n)
#define asort(x) sort(x.begin(),x.end())
#define dsort(x,t) sort(x.begin(),x.end(),greater<t>())
#define vuniq(x) x.erase(unique(x.begin(), x.end()), x.end())

#define pb(a) push_back(a)
#define mp(a,b) make_pair(a,b)

int main() {
    ll N,D; cin >> N >> D;
    double S[11][11];
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < D; j++) {
            cin >> S[i][j];
        }
    }
    ll cnt = 0;
    for (int i = 0; i < N; i++) {
        for (int j = i+1; j < N; j++) {
            double ans = 0;
            for (int k = 0; k < D; k++) {
                ans += (S[i][k]-S[j][k]) * (S[i][k]-S[j][k]);
            }
            ans = sqrt(ans);
            if(floor(ans) == ans){
                cnt++;
            }
        }
    }
    cout << cnt << endl;
}