Moving Robots

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