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)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n : u32 = read();

    for i in 1..n+1
    {
        let mut count = 0;

        for x in 1..n+1
        {
            let mut is_yz_1 = false;

            for y in 1..n+1
            {
                let mut is_z_1 = false;

                for z in 1..n+1
                {
                    // let ret = x.pow(2)+y.pow(2)+z.pow(2)+x*y+y*z+z*x;
                    let ret = (x+y+z)*(x+y+z)-x*y-y*z-z*x;
                    // eprintln!("  ({}) : ({},{},{}) -> {}", i, x, y, z, ret);

                    
                    if ret == i
                    {
                        count += 1;
                        // z_add = true;
                    }
                    else if ret > i
                    {
                        if z == 1
                        {
                            is_z_1 = true;

                            if y == 1
                            {
                                is_yz_1 = true;
                            }
                        }
                        break;
                    }
                }
                
                if is_z_1
                {
                    break;
                }
            }

            if is_yz_1
            {
                break;
            }
        }

        println!("{}", count);
    }
}