Thimbles#5896
In the game "3 Thimbles," the probability of correctly guessing the thimble hiding the seed is . Each correct guess earns the player lars, while each incorrect guess results in a loss of lar.
Your task is to calculate the probability that the player will run out of funds, starting with an initial amount of lars. Once the player's funds are depleted, they can no longer continue playing.
The input consists of a single line containing an integer (0 \leq N \leq 50), representing the initial amount of lars the player has.
Output a single line with the probability that the player will run out of funds, rounded to seven decimal places.
Example 1