When Things Don't Go as Planned, That's When Life Gets Interesting.

Hmm, let's see... Oh, so this roulette runs on prime numbers? Here's roughly how it works.

• In each round, I start with an integer $x = r_i$.

• Once a round begins, I can choose one of two actions on each turn.

  • Spin the roulette once more to change the current value of $x$.
  • End the round and earn points equal to the current value of $x$.

• If I spin the roulette, $x$ changes according to prime numbers. Specifically—

  • If $x$ is prime, it becomes $2x + 1$.

  • If $x$ is not prime, it becomes one of the prime divisors of $x$... The probability of each prime being selected is proportional to its multiplicity in the prime factorization of $x$.

    • For example, if $$, then , so it becomes with probability and with probability .

• After all rounds are over, the points earned in each round are added together to get the final score.

There are $N$ rounds in total, and I know the starting value of $x$ in each round... So if I play the roulette in a way that maximizes my expected score, winning this game is as good as guaranteed! Nihahaha~

Time limit

2000 ms

Memory limit

1024 MB

Checker

CUSTOM