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.

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.

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.

Sample Input 1

3
1 2 2
1 2

Sample Output 1

3

We have m=2. After two operations, A will be one of the following three sequences.

• A=(1,0,0): we end up with this after operations with (i,j)=(2,3) and (i,j)=(2,3).
• A=(0,1,0): we end up with this after operations with (i,j)=(1,3) and (i,j)=(2,3).
• A=(0,0,1): we end up with this after operations with (i,j)=(1,2) and (i,j)=(2,3).

Sample Input 2

4
1 1 1 1
2 2 2

Sample Output 2

1

Note that we do not distinguish two scenarios with different contents of B if the contents of A are the same.

Sample Input 3

4
2 2 3 4
3 1 4

Sample Output 3

3

见题面 Input 部分

见题面 Output 部分