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 Rust (1.15.1) (judge verdict: Accepted)

use std::io;
use std::str::FromStr;

fn input_int_tuple() -> (i32, i32) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<i32> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn input_f64_vec() -> Vec<f64> {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.split_whitespace().map(|s| s.parse().unwrap()).collect()
}

fn is_integer_distance(p1: &Vec<f64>, p2: &Vec<f64>) -> bool {
    let mut sum = 0f64;
    for i in 0..p1.len() {
        sum += (p1[i] - p2[i]) * (p1[i] - p2[i]);
    }
    sum = sum.sqrt();
    //println!("sum = {}", sum);
    (sum - sum.round()).abs() < 1e-6
}

fn main() {
    let (n, _) = input_int_tuple();
    let mut points: Vec<Vec<f64>> = Vec::new();
    for _ in 0..n {
        let x = input_f64_vec();
        points.push(x);
    }

    let mut sum = 0;
    for i in 0..(n as usize) {
        for j in (i+1)..(n as usize) {
            //println!("{}-{}", i, j);
            if is_integer_distance(&points[i], &points[j]) {
                sum += 1;
            }
        }
    }

    println!("{}", sum);

}