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: Wrong Answer)

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t.take(n).each { puts _1 }
# pp (1..n).map { |p|
#   l = []
#   pi = Math.sqrt(p).ceil
#   (1..pi).each { |x|
#     next if x * x + 2 * x + 3 > p
#     (1..pi-x).each { |y|
#       next if x * x + y * y + 1 + x * y + y + x > p
#       (1..pi-x-y).each { |z|
#         next unless x * x + y * y + z * z + x * y + y * z + z * x == p
#         l << [x, y, z]
#       }
#     }
#   }
#   l.uniq.count
# }