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 Go (1.6) (judge verdict: Wrong Answer)

// Package main provides
//
// File:  main.go
// Author: ymiyamoto
//
// Created on Thu Jul 11 07:43:17 2019
//
package main

import (
	"fmt"
	"math"
)

const eps = 1e-9

func main() {
	var n, d int
	fmt.Scan(&n, &d)

	xs := make([][]float64, n)
	for i := range xs {
		xs[i] = make([]float64, d)
		for j := range xs[i] {
			fmt.Scan(&xs[i][j])
		}
	}
	var ans int
	for i := range xs {
		for j := i + 1; j < len(xs); j++ {
			total := 0.0
			for k := range xs[i] {
				d := xs[i][k] - xs[j][k]
				total += d * d
			}
			math.Sqrt(total)
			if float64(int64(total))-eps <= total && total <= float64(int64(total))+eps {
				ans++
			}
		}
	}
	fmt.Println(ans)
}