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

Input

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

Output

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

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.

Sample Input 1

1+2*34

Sample Output 1

197

The cases where $\mathrm{eval}(S_{i..j})$ is not zero are as follows:

• $\mathrm{eval}(S_{1..1}) = 1$
• $\mathrm{eval}(S_{1..3}) = 1 + 2 = 3$
• $\mathrm{eval}(S_{1..5}) = 1 + 2 \times 3 = 7$
• $\mathrm{eval}(S_{1..6}) = 1 + 2 \times 34 = 69$
• $\mathrm{eval}(S_{3..3}) = 2$
• $\mathrm{eval}(S_{3..5}) = 2 \times 3 = 6$
• $\mathrm{eval}(S_{3..6}) = 2 \times 34 = 68$
• $\mathrm{eval}(S_{5..5}) = 3$
• $\mathrm{eval}(S_{5..6}) = 34$
• $\mathrm{eval}(S_{6..6}) = 4$

The sum of these is 1+3+7+69+2+6+68+3+34+4 = 197.

Sample Input 2

338333833338333338+333333833333338+333333338

Sample Output 2

527930018

见题面 Input 部分

见题面 Output 部分