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.Scan(&N)
	var result int
	for n := 1; n <= N; n++ {
		result = 0
		tmp := int(math.Pow(float64(n), 0.5))
		for x := 1; x <= tmp; x++ {
			for y := 1; y < tmp; y++ {
				for z := 1; z <= tmp; z++ {
					equal, over := xyzEqualn(x, y, z, n)
					if over {
						break
					}
					if equal {
						result += 1
					}
				}
			}
		}
		fmt.Println(result)
	}

}

func xyzEqualn(x, y, z, n int) (equal bool, over bool) {
	target := int(math.Pow(float64(x), 2.0)) + int(math.Pow(float64(y), 2.0)) + int(math.Pow(float64(z), 2.0)) + x*y + y*z + z*x
	if target > n {
		return false, true
	}
	if target == n {
		return true, false
	}
	return false, false
}