You are given a string $$$s$$$, consisting of digits from $$$0$$$ to $$$9$$$. In one operation, you can pick any digit in this string, except for $$$0$$$ or the leftmost digit, decrease it by $$$1$$$, and then swap it with the digit left to the picked.

For example, in one operation from the string $$$1023$$$, you can get $$$1103$$$ or $$$1022$$$.

Find the lexicographically maximum string you can obtain after any number of operations.

Input format:
The first line of the input consists of an integer $$$t$$$ ($$$1 \le t \le 10^4$$$)  — the number of test cases.

Each test case consists of a single line consisting of a digital string $$$s$$$ ($$$1 \le |s| \le 2\cdot 10^5$$$), where $$$|s|$$$ denotes the length of $$$s$$$. The string does not contain leading zeroes.

It is guaranteed that the sum of $$$|s|$$$ of all test cases doesn't exceed $$$2\cdot 10^5$$$.
Output format:
For each test case, print the answer on a separate line.
Example Input 0:
6
19
1709
11555
51476
9876543210
5891917899

Example Output 0:
81
6710
33311
55431
9876543210
7875567711

Notes:
In the first example, the following sequence of operations is suitable: $$$19 \rightarrow 81$$$.

In the second example, the following sequence of operations is suitable: $$$1709 \rightarrow 1780 \rightarrow 6180 \rightarrow 6710$$$.

In the fourth example, the following sequence of operations is suitable: $$$51476 \rightarrow 53176 \rightarrow 53616 \rightarrow 53651 \rightarrow 55351 \rightarrow 55431$$$.

Example input:
6
19
1709
11555
51476
9876543210
5891917899


Example output:
81
6710
33311
55431
9876543210
7875567711