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: Wrong Answer

Solution code:
### Problem C
import math

N = int(input())
rt = []

for i in range(1,N+1):
    rt.append(int(math.sqrt(i)))


for x in range(0,N):
    cnt = 0
    for i in range(1,rt[x]):
        for j in range(1,rt[x]):
            for k in range(1,rt[x]):
                if (i + j + k)**2 == x + (i*j + j*k + k*i):
                    cnt += 1
    print(cnt)

Submission status: Wrong Answer

Solution code:
N = int(input())
L = [0] * N

for x in range(1, 101):
    for y in range(x, 101):
        for z in range(y, 101):
            calc = x**2 + y**2 + z**2 + x*y + y*z + z*x
            if calc > N:
                break
            L[calc-1] += 1
            if x == y and y != z:
                L[calc-1] += 2
            elif x == z and x != y:
                L[calc-1] += 2
            elif y == z and x != y:
                L[calc-1] += 2

for l in L:
    print(l)