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)

use std::collections::HashMap;
use std::f64;

#[allow(unused)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
#[allow(unused)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
#[allow(unused)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
#[allow(unused)]
fn round_to_integer(a: f64, digit: u8) -> i64 {
    let mut ai: i64;
    let mut d = digit;
    let mut p = 1;

    while d > 0 {
        p *= 10;
        d -= 1;
    }
    ai = (a * p as f64) as i64;

    while ai as f64 / p as f64 - a > 0.5 / p as f64 {
        ai -= 1;
    }
    while ai as f64 / p as f64 - a < -0.5 / p as f64 {
        ai += 1;
    }
    ai
}

fn main() {
    input! {
        N:usize,
    }

    let mut counter = 0;

    for i in 1..(N + 1) {
        let mut x: u16;
        let mut y: u16;
        let mut z: u16;
        let mut di: f64 = i as f64;
        let mut counter: u16 = 0;
        for x in 1..(di.sqrt().round() as u16 + 1) {
            //let mut found = false;
            for y in (1..(di.sqrt().round() as u16 + 1)).rev() {
                for z in (1..(di.sqrt().round() as u16 + 1)).rev() {
                    if check(i as u16, x, y, z) {
                        counter += 1;
                        //println!("{}:({},{},{})", i, x, y, z);
                    }
                }
            }
        }
        println!("{}", counter);
    }
}

fn check(n: u16, x: u16, y: u16, z: u16) -> bool {
    n == x * x + y * y + z * z + x * y + y * z + z * x
}