B' 2^n teams participate in a playoff tournament. The tournament consists of 2^n - 1 games. They are held as follows: in the first phase of the tournament, the teams are split into pairs: team 1 plays against team 2 , team 3 plays against team 4 , and so on (so, 2^{n-1} games are played in that phase). When a team loses a game, it is eliminated, and each game results in elimination of one team (there are no ties). After that, only 2^{n-1} teams remain. If only one team remains, it is declared the champion; otherwise, the second phase begins, where 2^{n-2} games are played: in the first one of them, the winner of the game " 1 vs 2 " plays against the winner of the game " 3 vs 4 ", then the winner of the game " 5 vs 6 " plays against the winner of the game " 7 vs 8 ", and so on. This process repeats until only one team remains. The skill level of the i -th team is p_i , where p is a permutation of integers 1 , 2 , ..., 2^n (a permutation is an array where each element from 1 to 2^n occurs exactly once). You are given a string s which consists of n characters. These characters denote the results of games in each phase of the tournament as follows: Let 's say that an integer x is winning if it is possible to find a permutation p such that the team with skill x wins the tournament. Find all winning integers. The first line contains one integer n ( 1 <= n <= 18 ). The second line contains the string s of length n consisting of the characters 0 and/or 1. Print all the winning integers x in ascending order. '...