Problem Statement

You are given a positive integer X with N digits in decimal representation. None of the digits of X is 0.
For a subset S of $\lbrace 1,2, \ldots, N-1 \rbrace$ , let f(S) be defined as follows.

See the decimal representation of X as a string of length N, and decompose it into |S| + 1 strings by splitting it between the i-th and (i + 1)-th characters if and only if $i \in$ S.
Then, see these |S| + 1 strings as integers in decimal representation, and let f(S) be the product of these |S| + 1 integers.

There are 2^{N-1} subsets of $\lbrace 1,2, \ldots, N-1 \rbrace ,$ including the empty set, which can be S. Find the sum of f(S) over all these S, modulo 998244353.

Input

The input is given from Standard Input in the following format:
N
X

Output

Print the answer.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• X has N digits in decimal representation, none of which is 0.
• All values in the input are integers.

Sample Input 1

3
234

Sample Output 1

418

For $S = \emptyset$, we have f(S) = 234.
For $S = \lbrace 1 \rbrace$, we have $f(S) = 2 \times 34 = 68$.
For $S = \lbrace 2 \rbrace$, we have $f(S) = 23 \times 4 = 92$.
For $S = \lbrace 1, 2 \rbrace$, we have $f(S) = 2 \times 3 \times 4 = 24$.
Thus, you should print 234 + 68 + 92 + 24 = 418.

Sample Input 2

4
5915

Sample Output 2

17800

Sample Input 3

9
998244353

Sample Output 3

258280134

见题面 Input 部分

见题面 Output 部分