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CSES Problem Set

Moving Robots


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CSES - Moving RobotsCSES - Moving Robots

Time limit:1.00 s Memory limit:512 MB

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.

Constraints
Example

Input:
10

Output:
23.120740