Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::iter::*;
#[allow(unused_imports)]
use std::*;

macro_rules! test {
    ($($input:expr => $output:expr),* $(,)*) => {
#[test]
        fn solve_test() {
            $(
                assert_eq!(solve($input), $output);
            )*
        }
    };
}
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut 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 mut $var = read_value!($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")
    };
}

macro_rules! stdin {
    () => {{
        use std::io::Read;
        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }};
}

fn main() {
    println!("{}", solve(&stdin!()));
}
fn solve(src: &str) -> String {
    input! {
        source = src,
        n:usize,
    }
    let mut out = String::with_capacity(n * 2);
    for v in 1..=n {
        out.push_str(&format!("{}\n", f(v)));
    }
    out
}

fn f(n: usize) -> usize {
    let n = n as u64;
    let v = (n as f64).sqrt() as u64 + 1;

    let mut c = 0;
    for x in 1..=v {
        let x2 = x.pow(2);
        if x2 < n {
            for y in 1..=v {
                let y2 = y.pow(2);
                let xy = x2 + y2 + x * y;
                if xy < n {
                    for z in 1..=v {
                        let r = xy + z.pow(2) + x * z + y * z;
                        if r == n {
                            c += 1;
                        }
                        if r > n {
                            break;
                        }
                    }
                } else {
                    break;
                }
            }
        } else {
            break;
        }
    }
    c
}

test! {
    "20" => include_str!("c1_out.txt"),
}