Statistics

A magician has invited you to play a game. For this game, the magician uses a special table. On the table there are three spots in a row. The spots are labeled 0, 1, and 2, in order. He places three hats onto the table, so that each hat covers one of the spots. He then takes a ball and places it under one of the hats. The hats are not transparent, so you cannot see the ball while it is under a hat. Next, the magician shuffles the hats by repeatedly swapping two adjacent hats. Each swap is done by sliding the hats along the table, never showing you the ball. Once the magician finishes swapping the hats, you have to guess the spot where the ball is.

You are given a String hats which describes the contents of the hats in the beginning of the game. The i-th character of hats is 'o' if the ball was initially on the spot i. Otherwise, the i-th character of hats is '.' (a period).

You are also given a int numSwaps. Assume that the magician swapped the hat that contained the ball exactly numSwaps times. Please remember that in our version of the game the magician always swaps two adjacent hats. Also, note that the total number of swaps in the game may be larger than numSwaps, because the magician may sometimes swap two hats that don't contain the ball.

Assume that the magician chose the swaps he makes uniformly at random. That is, in each turn with probability 50% he swapped the hats on spots 0 and 1, and with probability 50% he swapped the hats on spots 1 and 2. Return the number of the spot that is most likely to contain the ball at the end of the game. If multiple spots are tied for the largest probability, return the smallest one of them.