Problem Statement

Given is a sequence $A$ of $N$ positive integers and a sequence $B$ of $N-1$ positive integers. You can do the following operation any number of times.

• Choose integers $i$ and $j$ ($1 \leq i < j \leq N$) and decrease each of the following values by $1$: $A_i,A_j,B_i,B_{i+1},\cdots,B_{j-1}$. Here, there should not be any negative value after this operation.

Let $m$ be the maximum number of operations that can be done. Find the number, modulo $998244353$, of sequences that $A$ can be after $m$ operations.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• $1 \leq B_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_{N-1}

Output

Print the answer.