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 kotlin.math.*
fun main() {
// 文字列
//    val str = readLine()!!
// 数値
    val n = readLine()!!.toInt()
// 行
//    val list = readLine()!!.split(" ").map(String::toInt)
//    val (a,b,c) = readLine()!!.split(" ").map(String::toInt)

//    val (a,b,c)="0 0 0".split(" ").map(String::toInt)

    val m= sqrt(n.toDouble()).toInt()
    for (o in 1..n) {
        var an = 0
        for (i in 1..m) {
            for (j in 1..m) {
                for (k in 1..m) {
                    val sum = i * i + j * j + k * k + i * j + j * k + k * i
                    if (o == sum) {
                        an++
                    }
                }
            }
        }
        println(an)

    }



//    print(str)
}