**Time limit:**1.00 s**Memory limit:**512 MB

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**

- $1 \le k \le 100$

**Example**

Input:

`10`

Output:

`23.120740`