Problem Statement

You are given an $N$-digit positive integer $X$. Find the number of "fragile multiples of $11$" less than or equal to $X$, modulo $998244353$.

Here, $x$ is called a "fragile multiple of $11$" if, for an integer $x$ greater than or equal to $10$, both of the following 2 conditions hold.

• $x$ is a multiple of $11$
• None of the positive integers formed by deleting $1$ digit from $x$, written in decimal without extra leading $0$s, is a multiple of $11$
  • Deleting the $2$nd digit from the top of $1234$, which is $2$, gives $134$
  • Deleting the $1$st digit from the top of $1023$, which is $1$, gives $023 = 23$

Constraints

• $1 \leq N \leq 100$
• $N$ is an integer
• $X$ is an $N$-digit positive integer
• The most significant digit of $X$ is not 0

Input

$N$
$X$

Output

Print the answer on $1$ line. Do not forget to output the remainder modulo $998244353$.

Sample

2
11

1

3
121

9

11
27775304230

1