Minimum Ternary String（CF-1009B）

Problem Description

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" →→ "100210";
"010210" →→ "001210";
"010210" →→ "010120";
"010210" →→ "010201".
Note than you cannot swap "02" → "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 aa is lexicographically less than string bb (if strings aa and bb have the same length) if there exists some position i (1≤i≤|a|, where |s||s| is the length of the string ss) such that for every j

Input

The first line of the input contains the string ss consisting only of characters '0', '1' and '2', its length is between 1 and 105 (inclusive).

Output

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

Examples

Input

100210

Output

001120

Input

11222121

Output

11112222

Input

20

Output

20

题意：给出一串只有 0、1、2 的数串，其中，0 与 1 可互相交换，1 与 2 可互相交换，求交换后最小的值

思路：无论 1 在哪，总能被换到 2 的前面去，但 0 无法换到 2 的前面，因此先统计第一个 2 前面 0 的个数，输出，然后再统计整个数串中 1 点个数，输出，最后再将第一个 2 后面的所有数字去掉 1 后输出

Source Program

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