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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
)

func f(n int) int {
	ans := 0
	for x := 1; x <= n; x++ {
		p := x*x
		if p > n {
			break
		}
		for y := 1; y <= n; y++ {
			q := p + y*y + x*y
			if  q > n {
				break
			}

			for z := 1; z <= n; z++ {
				r := q + z*z + y*z + z*x
				if r > n {
					break
				}

				if r == n {
					ans++
				}
			}
		}
	}
	return ans
}

func solve(n int) []int {
	ans := make([]int, n)

	for i := 1; i <= n; i++ {
		ans = append(ans, f(i))
	}

	return ans
}

func main() {
	var N int
	fmt.Scan(&N)

	result := solve(N)
	for _, i := range result {
		fmt.Println(i)
	}
}