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 Lua (LuaJIT 2.1.0) (judge verdict: Time Limit Exceeded)

-- 答え参照
local function xyz(x, y, z)
	return x*x + y*y + z*z + x*y + y*z + z*x
end

local N = io.read("*n")

local loop_num = math.ceil(math.sqrt(N)^3)

local out_s = {}
for i = 1, N do
	out_s[i] = 0
end

for x = 1, loop_num do
	for y = 1, loop_num do
		for z = 1, loop_num do
			local result = xyz(x, y, z)
			if result <= N then
				out_s[result] = out_s[result] + 1
			end
		end
	end
end

print(table.concat(out_s, "\n"))