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