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: Time Limit Exceeded)

#![allow(dead_code)]
#![allow(unused_imports)]
#![allow(non_camel_case_types)]
#![allow(non_snake_case)]
use ascii::{AsciiChar, AsciiStr, AsciiString};
use indexmap::IndexMap;
use itertools::*;
use libm::*;
use num::*;
use ordered_float::OrderedFloat;
use permutohedron::LexicalPermutation;
use proconio::marker::{Bytes, Chars};
use proconio::{fastout, input};
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::mem::swap;

fn count(p:(usize,usize,usize)) -> usize {
    let (x,y,z) = p;
    if x == y && y == z {
        1
    } else if x == y || y == z {
        3
    } else {
        6
    }
}

fn solve(n:usize) -> usize {
    let mut ret = 0;

    for x in 1..=n {
        if x*x > n {break}
        for y in x..=n {
            if x*x+y*y+x*y > n {break}
            for z in y..=n {
                if x*x+y*y+z*z+x*y+y*z+z*x == n {
                    ret += count((x,y,z))
                }
            }
        }
    }
    ret
}

fn main() {
    input!(n:usize);
    for i in 1..=n {
        println!("{}", solve(i));
    }
}