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.



Sample input:
20


Sample output:
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

Submission status: Time Limit Exceeded

Solution code:
import math
available_set = 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n = int(input())
# n = 10 ** 4
for i in range(1,n+1) :
    if (i not in available_set) :
        # print("well-known", i)
        print(0)
        continue
    
    c = 0
    # print("i", i)
    lim = math.floor(n / 3)
    for x in range(1,lim) :
        powx = pow(x,2)
        for y in range(x,lim) :
            powy = pow(y,2)
            if (powx + powy > i) :
                break

            for z in range(y, lim) :
                # x <= y <= zなので、、、
                o = powx + powy + pow(z,2) + x * y + y * z + z * x
                if (o > i) :
                    break
                # print("xyzon",x,y,z,o,n)
                if (o == i) :
                    tmp = {x,y,z}
                    # print("len", len(tmp))
                    if (len(tmp) == 1) :
                        c += 1
                    if (len(tmp) == 2) :
                        c += 3
                    if (len(tmp) == 3) :
                        c += 6

    print(c)