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 Scala (2.13.1) (judge verdict: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    val input      = scala.io.StdIn.readInt
    val sqrt_input = Math.sqrt( input ).toInt

    var map: Map[ Int, Int ] = Map.empty

    ( 1 to input ).foreach{ i =>
      map += ( i -> 0 )
    }

    ( 1 to sqrt_input ).foreach{ x =>
      ( 1 to sqrt_input ).foreach{ y =>
        ( 1 to sqrt_input ).foreach{ z =>
          val calc_num = x*x + y*y + z*z + x*y + y*z + z*x
          if( calc_num <= input ) {
            map += ( calc_num -> ( map( calc_num ) + 1 ) )
          }
        }
      }
    }

    ( 1 to input ).foreach{ i =>
      println( map( i ) )
    }
  }
}