The only difference between easy and hard versions is the length of the string. You can hack this problem only if you solve both problems.

Kirk has a binary string $s$ (a string which consists of zeroes and ones) of length $n$ and he is asking you to find a binary string $t$ of the same length which satisfies the following conditions:

• For any $l$ and $r$ ($1 \leq l \leq r \leq n$) the length of the longest non-decreasing subsequence of the substring $s_{l}s_{l+1} \ldots s_{r}$ is equal to the length of the longest non-decreasing subsequence of the substring $t_{l}t_{l+1} \ldots t_{r}$;
• The number of zeroes in $t$ is the maximum possible.

A non-decreasing subsequence of a string $p$ is a sequence of indices $i_1, i_2, \ldots, i_k$ such that $i_1 \lt i_2 \lt \ldots \lt i_k$ and $p_{i_1} \leq p_{i_2} \leq \ldots \leq p_{i_k}$. The length of the subsequence is $k$.

If there are multiple substrings which satisfy the conditions, output any.

Input

The first line contains a binary string of length not more than $2\: 000$.

Output

Output a binary string which satisfied the above conditions. If there are many such strings, output any of them.

Note

In the first example:

• For the substrings of the length $1$ the length of the longest non-decreasing subsequnce is $1$;
• For $l = 1, r = 2$ the longest non-decreasing subsequnce of the substring $s_{1}s_{2}$ is $11$ and the longest non-decreasing subsequnce of the substring $t_{1}t_{2}$ is $01$;
• For $l = 1, r = 3$ the longest non-decreasing subsequnce of the substring $s_{1}s_{3}$ is $11$ and the longest non-decreasing subsequnce of the substring $t_{1}t_{3}$ is $00$;
• For $l = 2, r = 3$ the longest non-decreasing subsequnce of the substring $s_{2}s_{3}$ is $1$ and the longest non-decreasing subsequnce of the substring $t_{2}t_{3}$ is $1$;

The second example is similar to the first one.