G. Expected Sum
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a number with $$$n$$$ digits. There is a possibility of $$$\frac{p_i}{100}$$$ that a plus sign is insert between the $$$i$$$-th digit from the left and the $$$(i+1)$$$-th digit from the left. The presence of every plus sign is independent. What is the expected sum of the expression?

Find the answer modulo $$$998244353$$$.

Input

The first line contains an integer $$$n$$$ $$$(2\leq n \leq 2 \times 10^6)$$$.

The second line contains the number you are given, with $$$n$$$ digits. There may be leading zeros.

The third line contains $$$n-1$$$ integers $$$p_1, p_2, \dots, p_{n-1}$$$ $$$(0 \leq p_i \leq 100$$$ for $$$1 \leq i \leq n-1$$$).

Output

Output a single line containing the answer modulo $$$998244353$$$.

Example
Input
2
26
50
Output
17