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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.InputStreamReader
import java.lang.Math.pow

fun main(args: Array<String>) {
    problem(InputStreamReader(System.`in`).useLines { block ->
        block.takeWhile {
            it.isNotEmpty()
        }.toList()
    })
}

fun problem(lines: List<String>) {
    val data: List<List<Int>> = lines.subList(1, lines.size).map { it.split(" ").map { it.toInt() } }
    var count = 0
    for (point1Index in 0 until data.size) {
        for (point2Index in (point1Index + 1) until data.size) {
            val point1 = data[point1Index]
            val point2 = data[point2Index]
//            println(point1 + ""+ point2)
            val sums = point2.mapIndexed { index, value ->
                pow(value.toDouble() - point1[index], 2.0)
            }.sum()
            val distance = Math.sqrt(
                sums
            )
            if ((distance == Math.floor(distance)) && !distance.isInfinite()) {
                count++
            }
        }
    }
    println(count)
}