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)

fn c() {

    input! {
        n: u64
    }

    let m = (n as f64).sqrt() as u32;

    for q in 1..=n {
        let mut count = 0;
        for x in 1..m {
            let x_sq = x.pow(2);
            for y in 1..=x {
                let y_sq = y.pow(2);
                for z in 1..=y {
                    let z_sq = z.pow(2);
                    let ans: u64 = (x_sq + y_sq + z_sq + x * y + y * z + z * x).into();
                    if ans == q {
                        let mut add = 1;
                        if x == y && y == z {
                            count += 1;
                        }
                        else if x == y || y == z {
                            count += 3;
                        }
                        else {
                            count += 6;
                        }
                    }
                }
            }
        }
        println!("{}", count);
    }
}

use proconio::{input, marker::Chars};

fn main() {
    c();
}