Each square of an $8 \times 8$ chessboard has a robot. Each robot independently moves $k$ steps, and there can be many robots on the same square.

On each turn, a robot moves one step left, right, up or down, but not outside the board. It randomly chooses a direction among those where it can move.

Your task is to calculate the expected number of empty squares after $k$ turns.

Input

The only input line has an integer $k$.

Output

Print the expected number of empty squares rounded to six decimal places (rounding half to even).

Constraints

• $1 \le k \le 100$

Example

Input:

10

Output:

23.120740