Description

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 ith 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.

Input

The first line contains a positive integer n(1 ≤ n ≤ 5∗10e5), which represents the number of the characters.

The second line contains n integers separated by spaces ai(1 ≤ ai ≤ 10e9), which represents the the combat power of the ith character.

Output

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 bi(b1 < b2 < …… < bm), which represents the the index of the characters who have the probability to stay till the end and become the final winner

5
1 2 30 16 1

2
3 4