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 parse_line<T: FromStr>() -> T {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn parse_pair<T: FromStr, U: FromStr>() -> (T, U) {
    let line = parse_line::<String>();
    let mut iter = line.split_whitespace();
    (
        iter.next().unwrap().parse().ok().unwrap(),
        iter.next().unwrap().parse().ok().unwrap(),
    )
}

fn parse_line_vec<T: FromStr>() -> Vec<T> {
    let line = parse_line::<String>();
    line.split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn println<T: std::string::ToString>(s: T) {
    println!("{}", s.to_string());
}

// ------------------------------------------------------------------------

type Point = Vec<i32>;

fn squared_magnitude(p1: &Point, p2: &Point) -> u32 {
    p1.into_iter()
        .zip(p2)
        .map(|(x1, x2)| (x1 - x2).pow(2) as u32)
        .sum::<u32>()
}

fn distance(p1: &Point, p2: &Point) -> f32 {
    (squared_magnitude(p1, p2) as f32).sqrt()
}

fn main() {
    let (n, _d) = parse_pair::<usize, usize>();

    let x: Vec<Point> = (0..n).map(|_| parse_line_vec()).collect();

    let valid_count = (0..n - 1)
        .map(|i| {
            (i + 1..n)
                .map(|j| distance(&x[i], &x[j]))
                .filter(|dist| dist.fract() == 0.0)
                .count()
        })
        .sum::<usize>();

    println(valid_count);
}