Minimum Ternary String

题意翻译

## 题目描述 给定一个由 '0', '1', '2' 组成的字符串 $S$ 。可以交换相邻'0', '1'或'1', '2'的位置（例如：'12' - '21' $\;$ '01' - '10'）请输出原字符串经过任意转换后字典序最小的字符串。原字符串长度不超过 $10^5$ 。 ## 输入格式 字符串 $S$ ### 输出格式 转化后字典序最小的字符串 Translated by @ZCDHJ

题目描述

You are given a ternary string (it is a string which consists only of characters '0', '1' and '2'). You can swap any two adjacent (consecutive) characters '0' and '1' (i.e. replace "01" with "10" or vice versa) or any two adjacent (consecutive) characters '1' and '2' (i.e. replace "12" with "21" or vice versa). For example, for string "010210" we can perform the following moves: - "010210" $ \rightarrow $ "100210"; - "010210" $ \rightarrow $ "001210"; - "010210" $ \rightarrow $ "010120"; - "010210" $ \rightarrow $ "010201". Note than you cannot swap "02" $ \rightarrow $ "20" and vice versa. You cannot perform any other operations with the given string excluding described above. You task is to obtain the minimum possible (lexicographically) string by using these swaps arbitrary number of times (possibly, zero). String $ a $ is lexicographically less than string $ b $ (if strings $ a $ and $ b $ have the same length) if there exists some position $ i $ ( $ 1 \le i \le |a| $ , where $ |s| $ is the length of the string $ s $ ) such that for every $ j < i $ holds $ a_j = b_j $ , and $ a_i < b_i $ .

输入输出格式

输入格式

The first line of the input contains the string $ s $ consisting only of characters '0', '1' and '2', its length is between $ 1 $ and $ 10^5 $ (inclusive).

输出格式

Print a single string — the minimum possible (lexicographically) string you can obtain by using the swaps described above arbitrary number of times (possibly, zero).

输入输出样例

输入样例 #1

100210

输出样例 #1

001120

输入样例 #2

11222121

输出样例 #2

11112222

输入样例 #3

20

输出样例 #3

20