Problem B
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 will appear as a substring in the Champernowne string at least once.

Given a string of digits and question marks, compute the smallest possible index that this string could appear as a substring in the Champernowne string by replacing each question mark with a single digit from $0$ to $9$. Each question mark can map to a different digit. Since this index can be large, print it modulo $998\, 244\, 353$.

Input

The first line of input contains a single integer $t$ $(1 \leq t \leq 10)$, which is the number of test cases.

Each of the next $t$ lines contains a string $s$ ($1 \leq |s| \leq 25$) consisting of digits $0$ to $9$ or question marks.

Output

Output $t$ lines. For each test case in order, output a single line with a single integer, which is the smallest possible index where the string could appear as a substring in the Champernowne string, modulo $998\, 244\, 353$.

9
0
???1
121
1?1?1
??5?54?50?5?505?65?5
000000000000
?2222222
?3????????9??8???????1??0
9?9??0????????????2

11
7
14
10
314159
796889014
7777
8058869
38886