Recently, Jvruo became obsessed with a fighting game. In this game, $n$ characters stand on an arena from left to right, and the combat power of the $i_{th}$ character is $a_i$. For each operation, Jvruo will choose two adjacent characters $x$ and $y$ on the arena for a duel. If $a_x> a_y$, then $x$ wins, if $a_x < a_y$, then $y$ wins. If $a_x = a_y$, then both $x$ and $y$ have a probability of $50\%$ to win. The victorious character will stay in the arena and double the combat power; the losing character will leave the arena.

Now Jvruo will perform $n−1$ operations, after $n−1$ operations, there will only be one character left in the ring. Obviously, Jvruo has $(n-1)!$ operation modes. In all these modes of operation, which characters have the probability to stay till the end and become the final winner.

The first line contains a positive integer $n(1 \le n \le 5 * 10^5)$, which represents the number of the characters.

The second line contains $n$ integers separated by spaces $a_i(1 \le a_i \le 10^9)$, which represents the the combat power of the $i_{th}$ character.

The first line contains a positive integer $m$, which represents the number of the characters who have the probability to stay till the end and become the final winner.

The second line contains $m$ integers in ascending order separated by spaces $b_i(b_1 < b_2 < …… < b_m)$, which represents the the index of the characters who have the probability to stay till the end and become the final winner.