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)

macro_rules! input {
     (source = $s:expr, $($r:tt)*) => {
         let mut iter = $s.split_whitespace();
         input_inner!{iter, $($r)*}
     };
     ($($r:tt)*) => {
         let s = {
             use std::io::Read;
         let mut s = String::new();
         std::io::stdin().read_to_string(&mut s).unwrap();
         s
     };
     let mut iter = s.split_whitespace();
     input_inner!{iter, $($r)*}
     };
}
     
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
 
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}
 
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
 
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
 
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
 
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
 
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::io::{stdout, Write, BufWriter};
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
//#[allow(unused_imports)]
//use proconio::marker::{Isize1, Usize1, Bytes, Chars};

//#[proconio::fastout]
fn main() {
    input!{
        n: usize,
        d: usize,
        points: [[i32; d]; n],
    }
    let mut ans = 0;
    for i in 0..(n - 1) {
        for j in (i + 1)..n {
            if is_square(points[i].iter().zip(points[j].iter())
                         .map(|(ci, cj)| (ci - cj).pow(2))
                         .sum()
                         ) { ans += 1; }
        }
    }
    println!("{}", ans);
}

type PositiveInt = i32;
fn is_square(n: PositiveInt) -> bool {
    n == ((n as f64).sqrt().floor() as PositiveInt).pow(2)
}