7675: [CSES Problem Set] Moving Robots
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Description
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.
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
$1≤k≤100$
Sample 1 Input
10
Sample 1 Output
23.120740