Score : $400$ points

Problem Statement

For a positive integer $n$, let $\mathrm{str}(n)$ be the string representing $n$ in decimal.

We say that a positive integer $n$ is periodic when there exists a positive integer $m$ such that $\mathrm{str}(n)$ is the concatenation of two or more copies of $\mathrm{str}(m)$. For example, $11$, $1212$, and $123123123$ are periodic.

You are given a positive integer $N$ at least $11$. Find the greatest periodic number at most $N$. It can be proved that there is at least one periodic number at most $N$.

You will get $T$ test cases to solve.

Constraints

• $1 \leq T \leq 10^4$
• $11 \leq N < 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$T$

$\mathrm{case}_1$

$\vdots$

$\mathrm{case}_T$

Each case is given in the following format:

$N$

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th test case.

3
1412
23
498650499498649123

1313
22
498650498650498650

For the first test case, the periodic numbers at most $1412$ include $11$, $222$, $1212$, $1313$, and the greatest is $1313$.