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.