A11584 | Largest Beautiful Number

Yes, that's another problem with definition of "beautiful" numbers.

Let's call a positive integer $x$ beautiful if its decimal representation without leading zeroes contains even number of digits, and there exists a permutation of this representation which is palindromic. For example, $4242$ is a beautiful number, since it contains $4$ digits, and there exists a palindromic permutation $2442$ .

Given a positive integer $s$ , find the largest beautiful number which is less than $s$ .

The first line contains one integer $t$ ( $1<=t<=10^{5}$ ) — the number of testcases you have to solve.

Then $t$ lines follow, each representing one testcase and containing one string which is the decimal representation of number $s$ . It is guaranteed that this string has even length, contains no leading zeroes, and there exists at least one beautiful number less than $s$ .

The sum of lengths of $s$ over all testcases doesn't exceed $2·10^{5}$ .

For each testcase print one line containing the largest beautiful number which is less than $s$ (it is guaranteed that the answer exists).