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.

$2^n$ 支队伍参加一场淘汰制锦标赛。该锦标赛共进行 $2^n - 1$ 场比赛，赛程安排如下：在锦标赛的第一阶段，所有队伍被两两配对：第 $1$ 队对阵第 $2$ 队，第 $3$ 队对阵第 $4$ 队，依此类推（因此该阶段共进行 $2^{n-1}$ 场比赛）。每场比赛的负方被淘汰，且每场比赛必有一支队伍被淘汰（无平局）。经过该阶段后，仅剩 $2^{n-1}$ 支队伍。若此时仅剩一支队伍，则该队被宣布为冠军；否则进入第二阶段，该阶段共进行 $2^{n-2}$ 场比赛：首场比赛由“第 $1$ 队 vs 第 $2$ 队”的胜者对阵“第 $3$ 队 vs 第 $4$ 队”的胜者，接着由“第 $5$ 队 vs 第 $6$ 队”的胜者对阵“第 $7$ 队 vs 第 $8$ 队”的胜者，依此类推。该过程持续进行，直至仅剩一支队伍。

第 $i$ 支队伍的实力值为 $p_i$，其中 $p$ 是整数 $1, 2, \dots, 2^n$ 的一个排列（即数组中 $1$ 至 $2^n$ 的每个整数恰好出现一次）。

给定一个长度为 $n$ 的字符串 $s$，其字符表示锦标赛各阶段的比赛结果，规则如下：

• 若 $s_i = 0$，则在第 $i$ 阶段（该阶段共进行 $2^{n-i}$ 场比赛）的每一场比赛中，实力值较低的队伍获胜；
• 若 $s_i = 1$，则在第 $i$ 阶段（该阶段共进行 $2^{n-i}$ 场比赛）的每一场比赛中，实力值较高的队伍获胜。

我们称一个整数 $x$ 是可获胜的（winning），如果存在某个排列 $p$，使得实力值为 $x$ 的队伍最终赢得整个锦标赛。请找出所有可获胜的整数。

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.

第一行包含一个整数 $n$（$1 \le n \le 18$）。

第二行包含一个长度为 $n$ 的字符串 $s$，由字符 0 和/或 1 组成。

Print all the winning integers $x$ in ascending order.

按升序输出所有获胜整数 $x$。