1730C · Minimum Notation

Problem: You have a string $s$ consisting of digits from $0$ to $9$ inclusive. You can perform the following operation any (possibly zero) number of times:

• You can choose a position $i$ and delete a digit $d$ on the $i$-th position. Then insert the digit $\min{(d + 1, 9)}$ on any position (at the beginning, at the end or in between any two adjacent digits).

What is the lexicographically smallest string you can get by performing these operations?

A string $a$ is lexicographically smaller than a string $b$ of the same length if and only if the following holds:

• in the first position where $a$ and $b$ differ, the string $a$ has a smaller digit than the corresponding digit in $b$.

Input Format: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then the test cases follow.

Each test case consists of a single line that contains one string $s$ ($1 \le |s| \le 2 \cdot 10^5$) — the string consisting of digits. Please note that $s$ is just a string consisting of digits, so leading zeros are allowed.

It is guaranteed that the sum of lengths of $s$ over all test cases does not exceed $2 \cdot 10^5$.

Output Format: Print a single string — the minimum string that is possible to obtain.

Note: In the first test case:

• Delete $8$ and insert $9$ at the end of the notation. The resulting notation is $04299$.
• Delete $4$ and insert $5$ in the $3$-rd position of the notation. The resulting notation is $02599$.

Nothing needs to be done in the second and third test cases.