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.
The only input line has an integer $k$ .
Print the expected number of empty squares rounded to six decimal places (rounding half to even).