Kirk and a Binary String (easy version)

1000ms

262144K

Description:

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 $$$i_1 < i_2 < \ldots < i_k$$$ 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.

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Sample Input:

0111001100111011101000

Sample Output:

0011001100001011101000

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.

Informação

Provedor Codeforces

Código CF1204D1