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"
	"math"
)

func main() {
	var n int
	fmt.Scanf("%d", &n)
	for i := 1; i <= n; i++ {
		ret := exec(i)
		fmt.Printf("%d\n", ret)
	}
}

func exec(n int) int {
	max := sqrt(n)
	var ret int
	for x := 1; x < max; x++ {
		for y := 1; y < max; y++ {
			for z := 1; z < max; z++ {
				if cal(x, y, z) == n {
					ret++
				}
			}
		}
	}
	return ret
}

func cal(x, y, z int) int {
	return x*x + y*y + z*z + x*y + x*z + y*z
}

func sqrt(p int) int {
	return int(math.Sqrt(float64(p)))
}