Flip and Reverse

2000ms

524288K

Description:

You are given a string $$$s$$$ of 0's and 1's. You are allowed to perform the following operation:

choose a non-empty contiguous substring of $$$s$$$ that contains an equal number of 0's and 1's;
flip all characters in the substring, that is, replace all 0's with 1's, and vice versa;
reverse the substring.

For example, consider $$$s$$$ = 00111011, and the following operation:

Choose the first six characters as the substring to act upon: 00111011. Note that the number of 0's and 1's are equal, so this is a legal choice. Choosing substrings 0, 110, or the entire string would not be possible.
Flip all characters in the substring: 11000111.
Reverse the substring: 10001111.

Find the lexicographically smallest string that can be obtained from $$$s$$$ after zero or more operations.

Input:

The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 5 \cdot 10^5$$$) — the number of test cases. Each of the following $$$T$$$ lines contains a single non-empty string — the input string $$$s$$$ for the respective test case.

All strings consist of characters 0 and 1, and their total length does not exceed $$$5 \cdot 10^5$$$.

Output:

For each test case, on a separate line print the lexicographically smallest string that can be obtained from $$$s$$$ after zero or more operations.

Sample Input:

Sample Output:

010110
0110110
10101010

Note:

In the first test case a single operation should be applied to the entire string.

In the second test case two operations are needed: 0111001, 0110110.

In the third test case the string stays the same after any operation.

Informação

Provedor Codeforces

Código CF1458D