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)

n=int(input())

num=[
0,
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1,
6,
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42,
9,
66,
30,
33,
18,
96,
0,
48,
18,
39,
36,
102,
12,
54,
18,
24,
9,
45,
24,
72,
30,
36,
0,
78,
6,
63,
36,
36,
21,
60,
9,
36,
12,
54,
24,
78,
27,
42,
0,
42,
18,
60,
9,
24,
24,
54,
39,
84,
0,
27,
36,
39,
12,
84,
0,
66,
0,
21,
30,
30,
42,
66,
18,
18,
18,
78,
12,
48,
42,
36,
0,
90,
6,
48,
33,
39,
24,
48,
15,
54,
15,
54,
24,
48,
18,
60,
0,
24,
0,
48,
24,
78,
24,
36,
9,
90,
12,
42,
24,
30,
45,
54,
0,
66,
12,
24,
12,
60,
6,
48,
33,
48,
0,
60,
6,
51,
54,
12,
0,
30,
0,
69,
21,
42,
15,
72,
15,
48,
21,
33,
36,
96,
6,
30,
0,
54,
6,
87,
30,
42,
30,
36,
13,
42,
6,
84,
48,
18,
18,
72,
0,
54,
12,
30,
30,
75,
24,
36,
24,
42,
18,
78,
12,
36,
30,
72,
0,
48,
6,
33,
36,
57,
36,
66,
6,
54,
0,
27,
36,
66,
12,
90,
0,
24,
3,
96,
24,
27,
24,
18,
24,
108,
12,
42,
48,
24,
18,
30,
0,
54,
18,
48,
12,
75,
18,
90,
21,
36,
12,
72,
12,
45,
24,
24,
0,
114,
0,
27,
30,
39,
33,
48,
12,
54,
12,
18,
42,
45,
27,
48,
0,
48,
6,
90,
9,
60,
42,
36,
12,
48,
0,
36,
42,
42,
18,
78,
0,
30,
6,
24,
33,
78,
9,
84,
30,
18,
15,
63,
18,
51,
30,
48,
0,
72,
6,
36,
51,
24,
30,
48,
21,
96,
6,
24,
6,
93,
12,
48,
0,
18,
6,
69,
18,
36,
18,
24,
18,
24,
6,
54,
36,
51,
33,
96,
0,
36,
15,
27,
30,
54,
30,
42,
12,
36,
0,
117,
36,
54,
36,
24,
0,
96,
3,
72,
36,
57,
27,
54,
6,
54,
21,
36,
12,
66,
33,
60,
0,
30,
24,
24,
15,
63,
30,
42,
24,
78,
9,
39,
30,
24,
24,
138,
0,
42,
0,
54,
24,
57,
12,
30,
24,
42,
18,
54,
6,
60,
33,
24,
0,
72,
6,
84,
24,
42,
6,
66,
15,
36,
0,
42,
48,
51,
18,
66,
0,
60,
3,
60,
12,
60,
57,
42,
9,
72,
12,
60,
42,
27,
24,
60,
0,
42,
18,
24,
30,
48,
30,
36,
18,
30,
9,
78,
12,
51,
18,
30,
0,
60,
0,
12,
57,
51,
18,
78,
6,
102,
12,
30,
24,
48,
27,
36,
0,
30,
12,
126,
6,
27,
36,
30,
18,
66,
0,
60,
30,
48,
36,
48,
0,
24,
6,
39,
24,
96,
12,
90,
33,
36,
6,
39,
6,
90,
27,
36,
0,
60,
12,
45,
42,
30,
30,
72,
12,
36,
9,
39,
36,
69,
24,
48,
0,
36,
6,
66,
15,
72,
39,
36,
27,
54,
18,
57,
30,
42,
12,
60,
0,
84,
24,
36,
27,
72,
12,
48,
21,
60,
0,
51,
30,
27,
30,
90,
0,
78,
0,
42,
57,
12,
30,
48,
18,
42,
6,
48,
24,
90,
15,
42,
0,
12,
15,
84,
24,
72,
18,
48,
21,
66,
3,
54,
42,
30,
24,
48,
0,
36,
18,
27,
12,
42,
9,
108,
18,
36,
12,
96,
24,
21,
30,
24,
0,
96,
9,
54,
18,
75,
30,
54,
18,
36,
0,
39,
18,
84,
18,
42,
0,
24,
6,
54,
18,
57,
42,
24,
9,
84,
18,
48,
42,
27,
30,
78,
0,
60,
0,
30,
48,
36,
6,
30,
36,
6,
10,
78,
12,
51,
48,
48,
0,
90,
0,
75,
9,
42,
24,
48,
15,
72,
12,
33,
42,
108,
12,
54,
0,
54,
18,
51,
42,
36,
48,
48,
12,
72,
0,
42,
18,
45,
30,
66,
0,
78,
3,
36,
15,
78,
30,
30,
30,
30,
15,
102,
12,
54,
18,
30,
0,
36,
6,
81,
48,
12,
24,
108,
6,
78,
18,
24,
36,
33,
18,
30,
0,
30,
0,
108,
21,
54,
42,
18,
18,
90,
6,
30,
48,
69,
36,
48,
0,
24,
15,
24,
15,
84,
24,
114,
6,
30,
0,
48,
6,
60,
42,
24,
0,
102,
12,
42,
42,
27,
21,
78,
9,
42,
24,
51,
24,
42,
12,
48,
0,
60,
12,
66,
6,
42,
24,
30,
24,
42,
0,
78,
24,
54,
12,
66,
0,
30,
6,
24,
51,
99,
18,
60,
24,
42,
18,
54,
6,
45,
60,
36,
0,
54,
6,
39,
39,
39,
30,
66,
18,
72,
0,
51,
24,
102,
12,
54,
0,
24,
0,
102,
12,
48,
24,
42,
36,
60,
0,
12,
48,
18,
12,
54,
0,
84,
18,
39,
9,
84,
30,
66,
18,
48,
15,
72,
48,
39,
42,
48,
0,
60,
0,
84,
30,
45,
33,
54,
6,
54,
30,
33,
30,
90,
6,
54,
0,
24,
6,
72,
27,
78,
12,
24,
15,
66,
0,
54,
36,
21,
42,
114,
0,
60,
3,
30,
33,
54,
27,
30,
33,
60,
6,
54,
12,
48,
33,
36,
0,
42,
12,
45,
39,
24,
36,
96,
18,
24,
12,
33,
18,
99,
18,
66,
0,
36,
0,
51,
24,
30,
30,
36,
15,
84,
6,
102,
48,
48,
18,
60,
0,
72,
12,
36,
42,
60,
12,
24,
21,
30,
0,
54,
18,
60,
18,
42,
0,
66,
6,
24,
24,
54,
15,
78,
12,
42,
27,
27,
30,
51,
27,
78,
0,
48,
6,
120,
27,
48,
42,
24,
12,
54,
6,
54,
24,
48,
36,
66,
0,
78,
9,
57,
21,
48,
18,
54,
33,
24,
30,
84,
18,
45,
33,
30,
0,
126,
9,
36,
30,
27,
30,
66,
18,
54,
0,
36,
42,
48,
6,
42,
0,
54,
6,
57,
12,
84,
54,
48,
6,
60,
6,
63,
18,
42,
36,
78,
0,
24,
24,
33,
24,
105,
24,
66,
27,
48,
0,
48,
30,
60,
30,
54,
0,
42,
3,
75,
48,
24,
12,
66,
12,
96,
6,
30,
12,
87,
21,
36,
0,
30,
24,
69,
12,
57,
30,
48,
24,
54,
0,
42,
54,
24,
24,
72,
0,
60,
0,
48,
24,
69,
24,
42,
18,
36,
12,
66,
24,
36,
42,
18,
0,
78,
9,
48,
36,
42,
42,
36,
12,
36,
21,
78,
18,
48,
12,
102,
0,
18,
12,
54,
24,
45,
27,
42,
13,
108,
12,
39,
24,
42,
27,
102,
0,
60,
6,
39,
24,
54,
12,
54,
24,
24,
0,
114,
24,
63,
48,
30,
0,
48,
6,
69,
36,
18,
12,
72,
6,
48,
18,
33,
54,
117,
12,
42,
0,
66,
12,
48,
6,
54,
36,
42,
21,
102,
6,
48,
54,
33,
30,
48,
0,
72,
0,
30,
24,
75,
24,
84,
30,
30,
0,
72,
18,
30,
42,
54,
0,
60,
12,
36,
45,
42,
12,
96,
6,
66,
0,
12,
36,
78,
36,
42,
0,
36,
0,
78,
24,
48,
24,
18,
30,
90,
15,
96,
18,
27,
21,
54,
0,
24,
21,
48,
27,
84,
18,
48,
42,
36,
6,
66,
12,
108,
12,
42,
0,
48,
9,
27,
60,
21,
36,
84,
6,
36,
18,
42,
18,
54,
18,
60,
0,
60,
15,
72,
9,
99,
42,
12,
12,
60,
0,
57,
42,
18,
18,
78,
0,
42,
6,
36,
36,
63,
9,
42,
15,
30,
18,
78,
6,
24,
48,
42,
0,
102,
12,
75,
45,
42,
30,
84,
24,
66,
9,
24,
30,
90,
24,
42,
0,
24,
3,
84,
21,
84,
33,
66,
24,
36,
6,
36,
48,
51,
18,
72,
0,
66,
18,
54,
30,
24,
18,
48,
18,
30,
0,
102,
12,
45,
36,
24,
0,
102,
3,
42,
15,
42,
54,
54,
21,
66,
24,
66,
30,
102,
3,
66,
0,
48,
12,
24,
30,
45,
36,
54,
6,
78,
9,
48,
24,
39,
36,
96,
0,
66,
6,
27,
27,
60,
30,
18,
30,
48,
12,
90,
24,
60,
36,
6,
0,
42,
12,
78,
36,
36,
24,
114,
6,
60,
0,
18,
6,
69,
18,
84,
0,
36,
6,
48,
6,
39,
24,
42,
24,
54,
6,
72,
48,
36,
42,
60,
0,
48,
0,
36,
18,
138,
24,
30,
30,
42,
18,
75,
18,
48,
18,
24,
0,
78,
0,
78,
57,
60,
9,
48,
9,
36,
30,
30,
42,
42,
39,
84,
0,
24,
12,
87,
27,
30,
42,
24,
24,
90,
0,
36,
24,
60,
36,
84,
0,
42,
0,
30,
21,
87,
12,
72,
24,
42,
12,
60,
30,
72,
21,
60,
0,
96,
12,
30,
42,
39,
18,
66,
12,
84,
12,
63,
42,
42,
24,
42,
0,
18,
6,
78,
15,
75,
45,
54,
12,
54,
6,
84,
30,
30,
18,
54,
0,
42,
24,
39,
27,
96,
18,
42,
21,
48,
0,
54,
18,
33,
36,
66,
0,
84,
0,
75,
48,
30,
42,
54,
12,
54,
15,
42,
30,
96,
18,
42,
0,
18,
6,
123,
15,
48,
24,
48,
39,
42,
6,
21,
54,
45,
12,
60,
0,
90,
12,
30,
36,
45,
18,
72,
21,
78,
12,
30,
12,
60,
30,
18,
0,
78,
6,
60,
36,
33,
18,
60,
12,
30,
0,
60,
18,
90,
30,
54,
0,
36,
1,
78,
27,
84,
30,
18,
15,
102,
9,
27,
30,
24,
57,
90,
0,
42,
9,
48,
42,
42,
12,
72,
27,
48,
9,
108,
18,
48,
48,
18,
0,
84,
6,
66,
24,
48,
21,
114,
6,
78,
24,
30,
30,
42,
18,
60,
0,
18,
12,
63,
9,
51,
66,
48,
15,
54,
0,
66,
60,
36,
18,
48,
0,
66,
6,
36,
30,
96,
9,
36,
30,
30,
24,
93,
24,
72,
24,
66,
0,
60,
24,
48,
30,
24,
30,
72,
6,
60,
12,
30,
12,
93,
18,
72,
0,
30,
0,
81,
30,
36,
48,
36,
30,
90,
6,
54,
24,
57,
24,
36,
0,
54,
18,
36,
24,
78,
18,
72,
33,
12,
0,
51,
30,
48,
24,
42,
0,
90,
3,
78,
30,
30,
27,
138,
6,
30,
18,
36,
24,
75,
24,
12,
0,
54,
12,
42,
18,
84,
36,
30,
18,
66,
6,
45,
36,
36,
48,
114,
0,
24,
6,
30,
21,
108,
15,
48,
18,
36,
18,
57,
24,
63,
42,
54,
0,
78,
6,
81,
36,
18,
24,
42,
18,
120,
0,
24,
24,
66,
12,
54,
0,
48,
12,
66,
18,
42,
36,
48,
18,
72,
6,
48,
48,
33,
6,
102,
0,
54,
24,
39,
54,
60,
12,
90,
18,
36,
3,
111,
24,
51,
48,
42,
0,
90,
0,
45,
36,
54,
48,
54,
24,
18,
18,
51,
18,
72,
0,
54,
0,
18,
12,
54,
36,
57,
18,
42,
18,
120,
0,
63,
42,
27,
36,
48,
0,
54,
6,
39,
30,
81,
18,
72,
33,
54,
9,
72,
12,
54,
54,
24,
0,
54,
15,
75,
24,
60,
12,
78,
6,
30,
12,
39,
54,
72,
6,
54,
0,
72,
6,
78,
12,
54,
39,
30,
15,
48,
6,
57,
48,
18,
24,
90,
0,
90,
18,
42,
24,
39,
42,
24,
30,
42,
0,
84,
6,
66,
30,
30,
0,
30,
0,
27,
42,
39,
33,
90,
24,
84,
18,
51,
36,
69,
24,
54,
0,
42,
18,
87,
33,
51,
18,
42,
9,
126,
9,
84,
36,
66,
18,
54,
0,
36,
0,
66,
12,
48,
15,
54,
30,
18,
18,
60,
18,
96,
54,
42,
0,
102,
0,
27,
36,
30,
36,
108,
15,
54,
0,
24,
36,
60,
24,
66,
0,
30,
0,
54,
15,
75,
48,
36,
18,
48,
24,
36,
36,
54,
15,
108,
0,
84,
18,
]

for i in range(n):
    print(num[i])