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: Accepted)

N,K=gets.chomp.split(' ').map{|n| n.to_i}
A = Array.new(10**6+1){0}

def getsum(a,b,c)
	return ((a+b)**2+(b+c)**2+(c+a)**2)/2
end
for a in 1..(10**2)
	for b in 1..a
		for c in 1..b
			if(a==b && b==c)
				A[getsum(a,b,c)] += 1
			elsif(a==b || b==c || c==a)
				A[getsum(a,b,c)] += 3
			else
				A[getsum(a,b,c)] += 6
			end
		end
	end
end

for i in 1..(N)
	puts A[i]
end