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.gets.chomp.to_i

def g(x, y, z)
	if x == 1
		return 1 + (y + z) + y * y + z * z + y * z
	else
		return g(x-1) + 2 * x + y + z - 1
	end
end

def a(n)
	ct = 0
	k = 0
	xb = Math.sqrt(n/6).to_i
	b = Math.sqrt(n).to_i
	(1..xb).each do |x|
		(x..b).each do |y|
			xy = x * x + y * y + x * y
			break if xy >= n
			(y..b).each do |z|
				c = xy + z * z + y * z + z * x
				if c == n
					if x == y && y == z
						ct += 1
					elsif x == y || y == z || z == x
						ct += 3
					else
						ct += 6
					end
					break
				elsif c > n
					y = b
					break
				end
			end
		end
	end
	return ct
end

(1..N).each do |n|
	puts a(n)
end