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_imports)]

use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::iter::once;
#[cfg(debug_assertions)]
include! {"./debug.rs"}

#[cfg(not(debug_assertions))]
macro_rules! debug {
    ($($arg:expr),*) => {};
}

macro_rules! read {
    ([$t:ident] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ([$t:ident]) =>
        (rl().split_whitespace().map(|w| read_type!(w, $t)).collect::<Vec<_>>());
    (_, [$t:ident] ; $n:expr) =>
        ((0..$n).map(|_| read!(_, [$t])).collect::<Vec<_>>());
    (_, [$t:ident]) =>
        (rl().split_whitespace().skip(1).map(|w| read_type!(w, $t)).collect::<Vec<_>>());
    ($($t:ident),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ($t:ident) => (read_type!(rl(), $t));
    ($($t:ident),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(read_type!(w.next().unwrap(), $t)),*)
    }};
}

macro_rules! read_type {
    ($s:expr, chars) => {
        $s.chars().collect::<Vec<char>>()
    };
    ($s:expr, usize1) => {
        read_type!($s, usize) - 1
    };
    ($s:expr, $t:ty) => {
        $s.parse::<$t>().unwrap()
    };
}

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

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}

////////////////////////////////////////////////////////////////////////////////

fn main() {
    let (n, d) = read!(usize, usize);
    let x = read!([i64]; n);

    let ans: usize = x
        .iter()
        .map(|ref v1| {
            x.iter()
                .map(|ref v2| {
                    debug!(v1, v2);
                    v1.iter()
                        .zip(v2.iter())
                        .map(|(&y, &z)| (y - z) * (y - z))
                        .fold(0, |sum, i| sum + i)
                })
                .filter(|&x| x != 0)
                .filter(|&x| {
                    let a = (x as f64).sqrt();
                    debug!(a);
                    a == a.floor()
                })
                .count()
        })
        .sum();

    println!("{}", ans / 2);
}