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)

fn main() {
    let mut reader = acio::Reader::new();
    let n = reader.read::<usize>();
    let d = reader.read::<usize>();
    let mut ps = vec![];
    for _ in 0..n {
        ps.push(reader.read_by::<f64>(d));
    }
    let mut c = 0;
    for i in 0..n {
        for j in (i + 1)..n {
            let mut p = 0.0;
            for k in 0..d {
                let s = ps[i][k] - ps[j][k];
                p += s * s;
            }
            let ps = p.sqrt();
            if ps.floor() == ps.ceil() {
                c += 1;
                //println!("{}-{} is it", i, j);
            } else {
                //println!("{}-{} is not", i, j);
            }
        }
    }
    println!("{}", c);
}

/// Mathematics Module
#[allow(dead_code)]
mod math {
    trait Math {
        fn lcm(v1: Self, v2: Self) -> Self;
        fn gcd(v1: Self, v2: Self) -> Self;
    }

    macro_rules! integer {
        ($t:ty) => {
            impl Math for $t {
                fn lcm(v1: $t, v2: $t) -> $t {
                    v1 * v2 / Self::gcd(v1, v2)
                }

                fn gcd(v1: $t, v2: $t) -> $t {
                    let (mut v1, mut v2) = (v1, v2);
                    while v1 != v2 {
                        if v1 < v2 {
                            v2 -= v1;
                        } else {
                            v1 -= v2;
                        }
                    }
                    v1
                }
            }
        };
    }

    integer!(i8);
    integer!(i16);
    integer!(i32);
    integer!(i64);
    integer!(isize);
    integer!(u8);
    integer!(u16);
    integer!(u32);
    integer!(u64);
    integer!(usize);
}

/// IO Module for AtCoder
#[allow(dead_code)]
mod acio {
    use std::fmt::Debug;
    use std::io::{stdin, Stdin};
    use std::str::FromStr;

    pub struct Reader {
        input: Stdin,
        stack: Vec<String>,
    }

    impl Reader {
        pub fn new() -> Self {
            Reader {
                input: stdin(),
                stack: vec![],
            }
        }

        pub fn read_by<F>(&mut self, count: usize) -> Vec<F>
        where
            F: FromStr,
            <F as FromStr>::Err: Debug,
        {
            let mut v = vec![];
            for _ in 0..count {
                v.push(self.read());
            }
            v
        }

        pub fn read<F>(&mut self) -> F
        where
            F: FromStr,
            <F as FromStr>::Err: Debug,
        {
            while self.stack.is_empty() {
                let mut line = self.read_line();
                self.stack.append(&mut line);
                self.stack.reverse();
            }
            self.stack.pop().unwrap().parse().unwrap()
        }

        fn read_line(&mut self) -> Vec<String> {
            let mut buf = String::new();
            self.input.read_line(&mut buf).unwrap();
            buf.split_whitespace().map(|s| s.to_string()).collect()
        }
    }
}