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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>//random,NULL
#include <string.h>
#include <time.h>
#include <unistd.h>//sleep()
#include <math.h>
#include <stdbool.h>

#define rep(i,n) for(int i=0; i<((int)n); i++)
#define REP(i,n) for(int i=0; i<=((int)n); i++)
#define srep(i,a,n) for(int i=a; i<((int)n); i++)
#define SREP(i,a,n) for(int i=a; i<=((int)n); i++)
#define rrep(i,n) for(int i=n-1; i>=0; i--)
#define RREP(i,n) for(int i=n; i>=0; i--)
#define INF 1000000000
const int mod = INF+7;

int main(){
  char buf[1024];
  int N,D;

  fgets(buf,sizeof(buf),stdin);
  sscanf(buf, "%d %d", &N, &D);

  int **X=(int **)malloc(sizeof(int *)*N);
  rep(i,N){
    X[i]=(int *)malloc(sizeof(int)*D);
  }

  rep(i,N){
    rep(j,D){
      scanf("%d",&X[i][j]);
    }
    int c=getchar();
  }

  // rep(i,N){
  //   rep(j,D){
  //     printf("%d ", X[i][j]);
  //   }
  //   printf("\n");
  // }

  int count=0;
  rep(i,N){
    srep(j,i+1,N){
      int dist=0;
      rep(k,D){
        dist+=(X[i][k]-X[j][k])*(X[i][k]-X[j][k]);
      }
      int dist2=sqrt(dist);
      if(dist==dist2*dist2){
        count++;
      }
    }
  }

  printf("%d\n", count);

  return 0;
}