CF1767D Playoff

$ 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: - if $ s_i $ is equal to 0, then during the $ i $ -th phase (the phase with $ 2^{n-i} $ games), in each match, the team with the lower skill level wins; - if $ s_i $ is equal to 1, then during the $ i $ -th phase (the phase with $ 2^{n-i} $ games), in each match, the team with the higher skill level wins. 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 \le n \le 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.