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)

#[allow(unused_macros)]
macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut iter = $s.split_whitespace();
            let mut next = || { iter.next().unwrap() };
            input_inner!{next, $($r)*}
        };
        ($($r:tt)*) => {
            let stdin = std::io::stdin();
            let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
            let mut next = move || -> String{
                bytes
                    .by_ref()
                    .map(|r|r.unwrap() as char)
                    .skip_while(|c|c.is_whitespace())
                    .take_while(|c|!c.is_whitespace())
                    .collect()
            };
            input_inner!{next, $($r)*}
        };
    }

#[allow(unused_macros)]
macro_rules! input_inner {
        ($next:expr) => {};
        ($next:expr, ) => {};

        ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
            let $var = read_value!($next, $t);
            input_inner!{$next $($r)*}
        };

        ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
            let mut $var = read_value!($next, $t);
            input_inner!{$next $($r)*}
        };
    }

#[allow(unused_macros)]
macro_rules! read_value {
        ($next:expr, ( $($t:tt),* )) => {
            ( $(read_value!($next, $t)),* )
        };

        ($next:expr, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        };

        ($next:expr, chars) => {
            read_value!($next, String).chars().collect::<Vec<char>>()
        };

        ($next:expr, bytes) => {
            read_value!($next, String).into_bytes()
        };

        ($next:expr, usize1) => {
            read_value!($next, usize) - 1
        };

        ($next:expr, $t:ty) => {
            $next().parse::<$t>().expect("Parse error")
        };
    }

fn main() {
    input! {
            n: usize,
            d: usize,
            matrix: [[i32; d]; n],
        }
    
    let mut ans = 0;

    for i in 0..n-1 {
        for j in i+1..n {
            let distance_square : i32 = (0..d).into_iter().map(|current_d| (matrix[i][current_d] - matrix[j][current_d]).pow(2)).sum();
            if ((distance_square as f64).sqrt().floor() as i32).pow(2) == distance_square {
                ans += 1;
            }
        }
    }

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