Problem Statement

You are given a string $S$. Each character of $S$ is one of 123456789+*, and the first and last characters of $S$ are digits. There are no adjacent non-digit characters in $S$.

For a pair of integers $i, j$ ($1 \leq i \leq j \leq |S|$), we define $\mathrm{eval}(S_{i..j})$ as follows:

• If both the $i$-th and $j$-th characters of $S$ are digits, then $\mathrm{eval}(S_{i..j})$ is the result of evaluating the $i$-th to the $j$-th characters (inclusive) of $S$ as a usual arithmetic expression (where * represents multiplication). For example, if $S =$ 1+2*151, then $\mathrm{eval}(S_{1..6}) = 1 + 2 \times 15 = 31$.
• Otherwise, $\mathrm{eval}(S_{i..j})$ is zero.

Find ${\displaystyle \sum_{i=1}^{|S|} \sum_{j=i}^{|S|} \mathrm{eval}(S_{i..j})}$, modulo $998244353$.

Constraints

• $1 \leq |S| \leq 10^6$
• Each character of $S$ is one of 123456789+*.
• The first and last characters of $S$ are digits.
• There are no adjacent non-digit characters in $S$.

Input

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

S

Output

Print ${\displaystyle \sum_{i=1}^{|S|} \sum_{j=i}^{|S|} \mathrm{eval}(S_{i..j})}$, modulo $998244353$.