Problem:
Score : 400 points

Problem Statement

Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range.
The mountain range consists of N mountains, extending from west to east in a straight line as Mt. 1, Mt. 2, ..., Mt. N.
Mr. Takahashi traversed the range from the west and Mr. Aoki from the east.

The height of Mt. i is h_i, but they have forgotten the value of each h_i.
Instead, for each i (1 ≤ i ≤ N), they recorded the maximum height of the mountains climbed up to the time they reached the peak of Mt. i (including Mt. i).
Mr. Takahashi's record is T_i and Mr. Aoki's record is A_i.

We know that the height of each mountain h_i is a positive integer.
Compute the number of the possible sequences of the mountains' heights, modulo 10^9 + 7.

Note that the records may be incorrect and thus there may be no possible sequence of the mountains' heights.
In such a case, output 0.

Constraints

1 ≤ N ≤ 10^5

1 ≤ T_i ≤ 10^9

1 ≤ A_i ≤ 10^9

T_i ≤ T_{i+1} (1 ≤ i ≤ N - 1)

A_i ≥ A_{i+1} (1 ≤ i ≤ N - 1)

Input

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

N
T_1 T_2 ... T_N
A_1 A_2 ... A_N

Output

Print the number of possible sequences of the mountains' heights, modulo 10^9 + 7.

Sample Input 1

5
1 3 3 3 3
3 3 2 2 2

Sample Output 1

4

The possible sequences of the mountains' heights are:

1, 3, 2, 2, 2

1, 3, 2, 1, 2

1, 3, 1, 2, 2

1, 3, 1, 1, 2

for a total of four sequences.

Sample Input 2

5
1 1 1 2 2
3 2 1 1 1

Sample Output 2

0

The records are contradictory, since Mr. Takahashi recorded 2 as the highest peak after climbing all the mountains but Mr. Aoki recorded 3.

Sample Input 3

10
1 3776 3776 8848 8848 8848 8848 8848 8848 8848
8848 8848 8848 8848 8848 8848 8848 8848 3776 5

Sample Output 3

884111967

Don't forget to compute the number modulo 10^9 + 7.

Sample Input 4

1
17
17

Sample Output 4

1

Some mountain ranges consist of only one mountain.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

class Main{
	public static void main(String[]$){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int[]a=new int[n],b=new int[n],min=new int[n],max=new int[n];
		Arrays.setAll(a,i->s.nextInt());
		Arrays.setAll(b,i->s.nextInt());
		Arrays.fill(min,1);
		Arrays.fill(max,Integer.MAX_VALUE);
		for(int i=0;i<n;++i) {
			if(i==0||a[i]!=a[i-1])
				min[i]=max[i]=a[i];
			else
				max[i]=Math.min(max[i],a[i]);
		}
		for(int i=n-1;i>=0;--i) {
			if(i==n-1||b[i]!=b[i+1]) {
				if(min[i]>b[i]||max[i]<b[i]) {
					System.out.println(0);
					return;
				}
				min[i]=max[i]=b[i];
			}else {
				max[i]=Math.min(max[i],b[i]);
			}
		}
		
		long r=1;
		for(int i=0;i<n;++i) {
			r*=Math.max(0,max[i]-min[i]+1);
			r%=1000000007;
		}
		System.out.println(r);
	}
}