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(
    non_snake_case,
    unused_variables,
    unused_assignments,
    unused_mut,
    unused_imports,
    dead_code
)]
//use permutohedron::LexicalPermutation as _;
use proconio::{fastout, input, marker::*};
use std::collections::*;
//use std::cmp::*;
//use std::num;
//use petgraph::unionfind::UnionFind;

#[fastout()]
fn main() {
    input! {
      mut N:usize
    }

    let mut ans = vec![0usize; N + 1];
    for x in 1..=100 {
        if N <= x * x {
            break;
        }
        for y in 1..=(N - x * x) {
            if N <= x * x + y * y {
                break;
            }
            for z in 1..=(N - x * x - y * y) {
                let t = x * x + y * y + z * z + x * y + y * z + z * x;
                if t <= N {
                    ans[t] += 1;
                }
            }
        }
    }

    for i in 1..=N {
        println!("{}", ans[i]);
    }
}