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 itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

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

    // x^2 + y^2 + z^2 + xy + yz + zx = (x+y+z)^2 - (xy + yz + zx)

    let mut t = vec![0; n + 1];

    for x in 1.. {
        if x * x > n {
            break;
        }
        for y in 1..=x {
            for z in 1..=y {
                let i = x * x + y * y + z * z + x * y + y * z + z * x;
                if i > n {
                    break;
                }
                if x != y && y != z {
                    t[i] += 6;
                } else if x == y && y == z {
                    t[i] += 1;
                } else {
                    t[i] += 3;
                }
            }
        }
    }

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