Champernowne Substring

The Champernowne string is an infinite string formed by concatenating the base-10 representations of the positive integers in order. It begins 1234567891011121314.... It can be proven that any finite string of digits appears as a substring in the Champernowne string at least once.

You are given a string made of digits and question marks. Replace each question mark with a single digit from $0$ to $9$. Find the smallest possible index at which the resulting string appears as a substring of the Champernowne string. Each question mark can be replaced with a different digit. The index can be large, so print it modulo $998\\,244\\,353$.

The first line contains a single integer $t$ $(1 \leq t \leq 10)$, the number of test cases. Each of the next $t$ lines contains a string $s$ $(1 \leq |s| \leq 25)$ made of the digits $0$ to $9$ and question marks.

For each test case, print one line with the smallest index modulo $998\\,244\\,353$.