Problem Statement

You are given $a sequence S_1,\ldots,S_N$ of length-M strings consisting of digits (0123456789) and ?.
There are 10^q ways to replace the occurrences of ? with digits independently, where q is the total number of ? in $S_1,\ldots,S_N. Among them, how many satisfy S_1\lt S_2 \lt \ldots \lt S_N$ when the resulting strings are seen as integers? Find this count modulo 998244353.
The resulting strings may have leading zeros. For instance, 0000000292 is seen as 292.

Input

The input is given from Standard Input in the following format:
N M
S_1
$\vdots$
S_N

Output

Print the answer.

Constraints

• $2 \leq N \leq 40$
• $1 \leq M \leq 40$
• N and M are integers.
• S_i is a string of length M consisting of digits and ?.

Sample Input 1

3 2
?0
??
05

Sample Output 1

4

Here are the four desired replacements.

• Replace the first character of S_1 with 0, and the first and second characters of S_2 with 0 and 1, respectively.
• Replace the first character of S_1 with 0, and the first and second characters of S_2 with 0 and 2, respectively.
• Replace the first character of S_1 with 0, and the first and second characters of S_2 with 0 and 3, respectively.
• Replace the first character of S_1 with 0, and the first and second characters of S_2 with 0 and 4, respectively.

Sample Input 2

2 1
0
0

Sample Output 2

0

Sample Input 3

10 10
1?22??37?4
1??8?0??49
3?02??8044
51?4?8?7??
5?9?20???2
68?7?6?800
?3??2???23
?442312158
??2??921?8
????5?96??

Sample Output 3

137811792

Find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分