CF1857B.Maximum Rounding

Given a natural number $x$ . You can perform the following operation:

• choose a positive integer $k$ and round $x$ to the $k$ -th digit

Note that the positions are numbered from right to left, starting from zero. If the number has $k$ digits, it is considered that the digit at the $k$ -th position is equal to $0$ .

The rounding is done as follows:

• if the digit at the $(k-1)$ -th position is greater than or equal to $5$ , then the digit at the $k$ -th position is increased by $1$ , otherwise the digit at the $k$ -th position remains unchanged (mathematical rounding is used).
• if before the operations the digit at the $k$ -th position was $9$ , and it should be increased by $1$ , then we search for the least position $k'$ ( $k'>k$ ), where the digit at the $k'$ -th position is less than $9$ and add $1$ to the digit at the $k'$ -th position. Then we assign $k=k'$ .
• after that, all digits which positions are less than $k$ are replaced with zeros.

Your task is to make $x$ as large as possible, if you can perform the operation as many times as you want.

For example, if $x$ is equal to $3451$ , then if you choose consecutively:

• $k=1$ , then after the operation $x$ will become $3450$
• $k=2$ , then after the operation $x$ will become $3500$
• $k=3$ , then after the operation $x$ will become $4000$
• $k=4$ , then after the operation $x$ will become $0$

To maximize the answer, you need to choose $k=2$ first, and then $k=3$ , then the number will become $4000$ .

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

Each test case consists of positive integer $x$ with a length of up to $2 \cdot 10^5$ . It is guaranteed that there are no leading zeros in the integer.

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

For each set of input data, output the maximum possible value of $x$ after the operations. The number should not have leading zeros in its representation.

In the first sample, it is better not to perform any operations.

In the second sample, you can perform one operation and obtain $10$ .

In the third sample, you can choose $k=1$ or $k=2$ . In both cases the answer will be $100$ .