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, marker::*};

fn main() {
    input! {
        n: usize
    };
    for i in 1..=n {
        let mut vecs = vec![];
        // x >= y >= z
        for x in 1..=i {
            let xx = x * x;
            if xx >= i {
                continue;
            }
            for y in 1..=x {
                let yy = y * y;
                let xy = x * y;
                if (xx + yy + xy) >= i {
                    continue;
                }
                for z in 1..=y {
                    let sum = xx + yy + z * z + xy + y * z + z * x;
                    if sum == i {
                        vecs.push(vec![x, y, z]);
                    } else if sum > i {
                        break;
                    }
                }
            }
        }
        let count = vecs.iter().fold(0, |acc, vec| {
            if (vec[0] == vec[1]) && (vec[1] == vec[2]) {
                acc + 1
            } else if (vec[0] == vec[1]) || (vec[1] == vec[2]) {
                acc + 3
            } else {
                acc + 6
            }
        });
        println!("{}", count);
    }
}