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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import math
N = int(input()) + 1
Nroot = int(math.sqrt(N)) - 1
for n in range(1,N):
    count = 0
    if n >= 6:
#        print(Nroot, int(math.pow(n,1/3))-1)
        for x in range(Nroot, int(math.pow(n,1/3))-1 , -1):
            for y in range(x,0,-1):
                if (x+2*y)**2 < n:
                    break
                for z in range(1,y+1):
#                    print((x + y + z)**2 - (x*y + y*z + z*x), n,x,y,z)
#                    print(x,y,z)
                    formula = (x + y + z)**2 - (x*y + y*z + z*x)
                    if formula == n:
                        if x == y and y == z:
                            count += 1
                        else:
                            count += 3
                        break

        print(count)
    else:
        print("0")