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: Time Limit Exceeded)

import java.lang.Math.pow
import kotlin.math.round
import kotlin.math.sqrt

fun main(){
    val n = readLine()!!.split(" ")[0].toInt()
    for (i in 1 until n + 1){
        var count = 0L
        val routN = sqrt(i.toDouble()).toInt() + 2
        for (x in 1 until routN + 1){
            for (y in 1 until routN + 1){
                for (z in 1 until routN + 1){
                    val kotae = x * x + y * y + z * z + x * y + y * z + z * x
                    if (z * z > i){
                        break
                    } else if (kotae > i){
                        break
                    } else if (kotae == i){
                        count++
                    }
                }
            }
        }
        println(count)
    }
}