As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:
Alice and Bob are going to play a famous game: Rock-paper-scissors. Both of them don’t like to think a lot, so both of them will use the random strategy: choose rock/paper/scissors in equal probability.
They want to play this game n times, then they will calculate the score s in the following way: if Alice wins a times, Bob wins b times, and in the remaining n−a−bgames they make a tie, the score will be the greatest common divisor of a and b.
Know Yuta wants to know the expected value of s×32n. It is easy to find that the answer must be an integer.
It is too difficult for Rikka. Can you help her?
Note: If one of a,b is 0, we define the greatest common divisor of a and b as a+b.