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 Python (3.8.2) (judge verdict: Accepted)

import sys,math
#DEBUG=True
DEBUG=False
if DEBUG:
    f=open("202007_2nd/C_input.txt")
else:
    f=sys.stdin
# Find the number of triples of integers (x,y,z) such that
# (x+y)**2 + (y+z)**2 + (x+z)**2 = 2*N
N=int(f.readline().strip())
ans=[0 for _ in range(N)]
I=int(math.sqrt(N))
for __ in range(I):
    A2=N-((__+1)**2)
    if A2<=0:
        break
    I2=int(math.sqrt(A2))
    for ___ in range(I2):
        A3=A2-((___+1)**2)
        if A3<=0:
            break
        I3=int(math.sqrt(A3))
        for ____ in range(I3):
            tmp=((__+___+2)**2)+((___+____+2)**2)+((__+____+2)**2)
            if tmp<=2*N:
                ans[int(tmp/2)-1]+=1
            else:
                break
for _ in range(N):
    print(ans[_])
f.close()