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A binary string $s$ is said to be antisymmetric if and only if $s[i] \neq s[|s| - i + 1]$ for all $i \in [1, |s|]$.
Yuta has $n$ binary strings $s_i$, and he wants to know the number of binary antisymmetric strings of length $2 L$ which contain all given strings $s_i$ as continuous substrings. Help him find that number. As the answer can be very large, find it modulo $998\,244\,353$.
The first line of the input contains two integers $n$ and $L$ ($1 \leq n \leq 6$, $1 \leq L \leq 100$).
Then $n$ lines follow, each line contains a string $s_i$ ($1 \leq |s_i| \leq 20$) consisting of characters "
0" and "
Print a single line with a single integer: the answer modulo $998\,244\,353$.
2 2 011 001
2 3 011 001
In the second example, the strings which satisfy all the restrictions are