Brief Story

Yasazo, a fan of the amateur baseball team "Spotted Grasshoppers", records the score of each inning of their games on cards and keeps them.
One day, Yasazo accidentally turned over the file holding the cards.
When it was turned over, $N$ cards fell out of the file. Yasazo picked up $9$ of the fallen cards and noticed that, when arranged appropriately, they form a combination whose game result is $4-33$.
Yasazo now wonders how many ways there are to pick up such a combination from the fallen cards. Please find the actual number of ways.

Problem Statement

You are given information about $N$ mutually distinguishable cards. The $i$-th card has $A_i$ written on its upper part and $B_i$ written on its lower part.
$A_i$ is a non-negative integer, and $B_i$ is one of the following: a non-negative integer, X (uppercase), or a string formed by appending X to (the decimal representation of) a positive integer.
From the $N$ cards, you choose $9$ cards for which a good scoreboard exists.
A good scoreboard is an arrangement of the $9$ cards that satisfies the following conditions.

Conditions for a good scoreboard:

• Arrange the cards in a horizontal row, and let $U_j$ and $D_j$ be what is written on the upper part and the lower part, respectively, of the $j\ (1\leq j\leq 9)$-th card from the left
• For $1\leq j\leq 8$, $D_j$ does not contain X
• Hereafter, let $d_9$ be the string obtained by removing as many X as possible from $D_9$, regarded as an integer (if the string becomes empty, let $d_9=0$)
• If $\displaystyle\sum_{k=1}^9U_k<\sum_{k=1}^8D_k+d_9$, then $D_9$ contains X, and if $d_9\neq0$, then $\displaystyle\sum_{k=1}^9U_k\geq \sum_{k=1}^8D_k+d_9-4$

Among the ways to choose $9$ cards for which a good scoreboard exists, find the number of ways such that the sum of the upper parts is $4$ and the sum of the lower parts is $33$.
More precisely, find the number of ways to choose $9$ cards for which there exists a good scoreboard satisfying $\displaystyle\sum_{k=1}^9U_k=4,\ \displaystyle\sum_{k=1}^8D_k+d_9=33$.
Since the answer can be very large, print the answer modulo $998244353$.

Input

$N$
$A_1\ A_2\ \dots\ A_N$
$B_1\ B_2\ \dots\ B_N$

• $9\leq N\leq 2000$
• $0\leq A_i\leq 4$
• $0\leq B_i\leq 33$, or $B_i=$X (uppercase), or $B_i$ is a string formed by appending X to (the decimal representation of) an integer satisfying $1\leq b\leq 33$
• All numerical values in the input are integers

Output

Print the answer modulo $998244353$.
Print a newline at the end.

Sample

14
1 0 1 0 0 2 0 1 0 3 0 0 1 0
2 7 1 8 2 8 1 8 2 8 4 5X 9X X

4

81
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X 0 0 0 0 0 0 0 0 1X

331646352

52
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 3 1 5X 1 1 0 0 0 5 0 3 X 0 1 0 2 0 0 7 0 0 0 2 0 1 0 0 0 0 0 0 7 1 10 2 0 0 1 X 5 4 0 1 0 0 0 2 X

228