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, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        n:usize,
    }
    let mut anss = vec![0; n + 1];
    for x in 1..=n {
        if x * x >= n {
            continue;
        }
        for y in 1..=n {
            if x * x + y * y + x * y > n {
                break;
            }
            // z*z + y*z + z*x = n
            // let z = n-x*x-y*y-x*y
            for z in 1..n {
                // if z * z + y * z + z * x + x * x + y * y + x * y == n {
                //     ans += 1;
                // }
                let s = x * x + y * y + z * z + x * y + x * z + y * z;
                if s > n {
                    break;
                } else {
                    anss[s as usize] += 1;
                }
            }
        }
    }
    for i in 1..=n {
        println!("{}", anss[i]);
    }
}