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: Wrong Answer)

import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Scanner;


public class Main {
	
	public static void main(String[] args){
		try(Scanner sc = new Scanner(System.in)){
			
			final int N = sc.nextInt();
			
			long[] left_height  = new long[N];
			long[] right_height = new long[N];
			for(int i = 0; i < N; i++){
				final long T = sc.nextLong();
				left_height[i] = T;
			}
			for(int i = 0; i < N; i++){
				final long A = sc.nextLong();
				right_height[i] = A;
			}
			
			boolean[] left_changed = new boolean[N];
			left_changed[0] = true;
			for(int i = 1; i < N; i++){
				if(left_height[i] != left_height[i - 1]){
					left_changed[i] = true;
				}
			}
			
			boolean[] right_changed = new boolean[N];
			right_changed[N - 1] = true;
			for(int i = N - 2; i >= 0; i--){
				if(right_height[i + 1] != right_height[i]){
					right_changed[i] = true;
				}
			}
			
			for(int i = 0; i < N; i++){
				if(left_changed[i] && right_changed[i] && left_height[i] != right_height[i]){
					System.out.println(0);
					return;
				}
			}
			
			long answer = 1;
			for(int i = 0; i < N; i++){
				if(left_changed[i] || right_changed[i]){ continue; }
				//System.out.println(i);
				answer *= (Math.min(left_height[i], right_height[i]));
				answer %= (1000000000 + 7);
			}
			
			System.out.println(answer);
		}
	}
}