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: Accepted

Solution code:
from collections import deque


def main():
    N = int(input())
    arr = deque(['0','0','0','0','0','1','0','0','0','0','3','0','0','0','0','0','3','3','0','0','0','0','0','1','6','0','3','0','0','0','0','0','3','3','6','0','0','3','0','0','0','0','3','3','6','0','6','0','0','0','3','0','0','1','6','0','6','6','0','0','6','0','0','0','0','3','3','3','6','0','6','3','6','0','0','0','6','0','0','0','3','3','9','0','6','3','6','0','3','6','0','0','0','0','6','1','6','0','6','6','0','3','12','0','6','0','0','3','6','0','0','0','3','3','12','0','6','3','6','0','3','6','9','0','6','0','0','0','3','6','3','3','6','0','6','3','12','0','3','6','6','0','6','0','6','3','6','0','0','1','6','3','12','6','0','0','12','0','6','0','6','6','12','0','0','6','0','0','6','0','12','3','6','0','6','3','9','6','3','6','6','0','6','0','6','0','15','6','0','0','6','0','3','3','12','0','12','6','6','0','3','6','6','3','12','0','6','0','9','6','0','0','6','3','12','1','6','6','6','6','0','0','18','0','12','0','3','6','12','0','0','6','3','6','12','0','12','0','0','0','9','3','9','6','12','3','12','0','3','6','6','0','12','0','12','0','9','9','0','0','6','3','6','3','12','6','9','3','6','0','12','3','6','3','9','6','12','6','6','0','6','0','9','6','6','0','12','3','6','0','9','6','6','1','6','0','21','12','6','0','12','0','12','0','0','6','15','6','0','6','12','0','12','0','12','0','0','0','12','0','12','12','3','3','18','3','6','3','6','6','9','9','18','0','6','0','12','0','9','6','0','3','12','3','6','6','12','6','6','0','0','0','15','3','18','3','18','3','12','6','3','6','9','0','12','0','12','0','18','12','0','0','12','3','6','0','6','6','9','6','0','0','18','1','18','3','12','6','6','6','12','0','15','6','12','6','18','0','0','6','0','9','12','0','18','0','6','3','12','0','12','12','0','0','12','0','3','6','12','6','18','9','18','0','9','6','18','0','6','0','6','3','27','6','6','6','6','3','6','0','12','6','9','0','6','0','18','0','9','9','15','3','12','6','6','3','9','6','12','12','18','0','18','0','6','6','21','6','0','0','6','3','15','6','12','6','18','0','0','0','12','6','6','3','6','4','18','6','12','6','3','9','30','0','18','0','6','6','12','6','6','9','12','0','18','6','18','0','6','0','12','0','6','12','6','3','18','0','6','6','6','6','15','3','24','0','6','3','18','0','12','6','12','6','24','0','15','18','9','6','0','0','18','3','6','0','15','12','12','6','6','0','18','0','6','3','12','0','12','6','6','9','9','6','24','3','24','0','9','12','6','6','12','0','12','0','21','9','15','6','12','3','18','3','12','6','12','6','0','0','12','0','12','6','24','0','6','12','6','1','9','6','12','6','24','0','18','3','12','6','6','12','24','0','12','6','15','6','18','0','18','0','0','0','18','9','21','12','0','6','18','0','9','6','6','6','12','0','12','0','9','9','27','6','6','3','18','6','21','6','6','12','12','0','12','0','24','12','0','0','24','3','24','6','12','12','18','0','0','0','12','0','18','3','15','6','12','9','6','0','15','6','9','12','24','0','12','3','6','6','21','6','18','3','18','0','21','12','15','6','6','0','12','3','12','9','18','9','12','6','6','6','24','0','18','3','24','0','6','6','0','6','9','6','6','4','30','0','18','12','9','6','24','0','18','0','9','12','21','6','6','12','12','0','18','0','21','15','12','0','12','6','12','12','18','0','18','0','6','0','9','12','18','6','30','0','0','0','24','6','9','3','12','6','30','3','6','12','6','12','12','0','36','0','6','3','27','12','12','6','6','6','24','0','12','6','12','0','18','0','18','15','18','3','18','6','12','6','6','12','3','6','6','0','12','3','39','3','12','12','12','3','18','0','21','12','21','6','18','0','12','0','9','9','12','9','24','9','12','6','12','6','33','0','6','0','18','0','9','15','12','6','24','6','6','3','15','6','15','12','18','0','18','1','18','6','12','6','6','0','24','6','24','12','18','6','24','0','6','6','12','15','24','0','24','6','6','0','18','0','15','18','12','0','24','0','12','6','12','12','18','6','24','0','0','6','24','3','12','0','12','6','30','9','6','12','24','12','12','0','15','18','12','0','18','0','24','6','15','6','18','3','18','3','12','6','24','12','12','12','6','0','36','0','18','3','6','12','6','9','12','0','3','12','36','0','30','0','12','0','18','6','12','9','12','6','24','3','18','12','15','9','24','0','18','6','18','9','18','12','6','6','24','3','24','0','12','12','12','0','6','0','27','12','18','3','30','3','18','6','0','12','15','6','18','0','24','0','9','6','9','12','18','7','24','0','24','12','15','12','24','0','24','0','6','9','30','9','6','6','0','9','33','12','36','0','12','0','18','0','6','21','12','6','36','6','0','3','18','6','12','6','24','0','12','3','24','6','9','12','6','6','30','6','18','12','9','9','12','0','30','3','18','3','27','6','30','12','12','0','24','0','27','12','6','0','24','3','18','18','9','6','18','0','12','3','33','18','12','9','6','0','12','6','30','0','24','12','12','0','30','6','6','6','0','6','24','0','12','0','18','15','33','6','30','15','18','0','9','12','24','9','12','0','18','6','27','18','15','6','18','3','24','0','6','6','36','12','18','0','12','3'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    for n in range(1, N + 1):
        print(arr.popleft())
if __name__ == "__main__":
    main()