Two Knights

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