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: Time Limit Exceeded)

package main

import (
	"fmt"
)

func main() {
	var N int
	fmt.Scan(&N)
	for n := 1; n <= N; n++ {
		ans := 0
		for x := 1; x <= N; x++ {
			if x*x > n {
				break
			}
			for y := 1; y <= N; y++ {
				if x*x+y*y > n {
					break
				}
				for z := 1; z <= N; z++ {
					if x*x+y*y+z*z > n {
						break
					}
					if x*x+y*y+z*z+x*y+y*z+z*x == n {
						ans++
					}
				}
			}
		}
		fmt.Println(ans)
	}
}