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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

N = $stdin.read.to_i
counts = Array.new(N) { 0 }
1.upto(N) {|x|
  x2 = x * x
  break if N < x2 + 5
  2.upto(N) {|y|
    y2 = y * y
    xy = x * y
    break if N < x2 + y2 + xy + 3
    next if x == y
    3.upto(N) {|z|
      next if x == z or y == z
      n = x * x + y * y + z * z + x * y + y * z + z * x
      counts[n - 1] += 3 if n <= N
    }
  }
}

1.upto(N) {|x|
  x2 = x * x
  break if N < 3 * x2 + 3
  1.upto(N) {|z|
    next if x == z
    n = 3 * x2 + z * z + 2 * x * z
    counts[n - 1] += 3 if n <= N
  }
}

1.upto(N) {|x|
  n = 6 * x * x
  counts[n - 1] += 1 if n <= N
}

puts counts.join("\n")