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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.nextInt()
    println(problem2020c(n))
}

fun problem2020c(n: Int): Int {
    var count = 0
    for (x in 1..n) {
        val x2 = x * x
        // ゾロ目
        if (x * x * 6 > n) break
        for (y in 1..n) {
            if (x * y * 6 > n) break
            val y2 = y * y
            for (z in 1..n) {
                if (x * z * 6 > n) break
                val z2 = z * z
//                debugLog(x, y, z, x2 + y2 + z2 + x * y + y * z + z * x, y2, x2 + y2 + z2 + x * y + y * z + z * x <= n)
                if (x2 + y2 + z2 + x * y + y * z + z * x <= n) count++
            }
        }
    }
    return count
}