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)

trait Integer {
    fn is_sqrt_int(&self) -> bool;
}

impl Integer for i64 {
    fn is_sqrt_int(&self) -> bool {
        let f = *self as f64;
        let sqrt = f.sqrt() as i64;
        *self / sqrt == sqrt && *self % sqrt == 0
    }
}

fn read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim_right().to_owned()
}

fn comb2(n: usize) -> Vec<(usize, usize)> {
    let mut v = Vec::new();
    for i in 0..(n - 1) {
        for j in (i + 1)..n {
            v.push((i, j));
        }
    }
    v
}

fn distance2(p0: &Vec<i64>, p1: &Vec<i64>) -> i64 {
    p0.iter().zip(p1.iter()).map(|(x0, x1)| (x0 - x1) * (x0 - x1)).sum()
}

fn main() {
    let nums: Vec<i64> = read_line().split_whitespace().map(|x| x.parse().unwrap()).collect();
    let (n, _) = (nums[0] as usize, nums[1]);
    let ps: Vec<Vec<i64>> = (0..n).map(|_| read_line().split_whitespace().map(|x| x.parse().unwrap()).collect()).collect();
    
    let count = comb2(n)
        .into_iter()
        .filter(|&(i, j)| distance2(&ps[i], &ps[j]).is_sqrt_int())
        .count();

    println!("{}", count);
}