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: Accepted)

#[allow(unused_imports)]
use std::{cmp::Reverse, collections::*};

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Chars, Usize1},
};

#[allow(unused_imports)]
use itertools::Itertools;

#[allow(unused_imports)]
use num::Integer;

fn f(x: usize, y: usize, z: usize) -> usize {
    x * x + y * y + z * z + x * y + y * z + z * x
}

fn g(
    n: usize,
    x: usize,
    y: usize,
    z: usize,
    map: &mut HashMap<usize, HashSet<(usize, usize, usize)>>,
) {
    let v = f(x, y, z);
    if v > n {
        return;
    }
    let set = map.entry(v).or_insert(HashSet::new());
    if set.contains(&(x, y, z)) {
        return;
    } else {
        set.insert((x, y, z));
    }
    g(n, x + 1, y, z, map);
    g(n, x, y + 1, z, map);
    g(n, x, y, z + 1, map);
    g(n, x + 1, y + 1, z, map);
    g(n, x + 1, y, z + 1, map);
    g(n, x, y + 1, z + 1, map);
    g(n, x + 1, y + 1, z + 1, map);
}

#[fastout]
pub fn main() {
    input! {
        n: usize,
    }

    let mut map = HashMap::new();
    g(n, 1, 1, 1, &mut map);

    for i in 1..=n {
        let v = map.entry(i).or_insert(HashSet::new()).len();
        println!("{}", v);
    }
}