Your task is to count for k=1,2,\ldots,n the number of ways two knights can be placed on a k \times k chessboard so that they do not attack each other.

Input

The only input line contains an integer n.

Output

Print n integers: the results.

Constraints

• 1 \le n \le 10000

Example

Input:

8

Output:

0
6
28
96
252
550
1056
1848