Periodic Number

AtCoder

IDarc141_a

Time2000ms

Memory256MB

Difficulty—

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: $N$ [samples]

Samples

Input #1

3
1412
23
498650499498649123

Output #1

1313
22
498650498650498650

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

API Response (JSON)

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