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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

class Main{
	public static void main(String[] args) throws Exception{
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(reader.readLine());
		String[] takaString = reader.readLine().split(" ",0);
		String[] aokiString = reader.readLine().split(" ",0);
		int[] taka = new int[n];
		for(int i = 0; i < n; i++) taka[i] = Integer.parseInt(takaString[i]);
		int[] aoki = new int[n];
		for(int i = 0; i < n; i++) aoki[i] = Integer.parseInt(aokiString[i]);

		int[] yama = new int[n];
		{
			int max = 0;
			for(int i = 0; i < n; i++) {
				if(max < taka[i]) {
					max = taka[i];
					yama[i] = taka[i];
				}
			}
		}
		{
			int max = 0;
			for(int i = n-1; i >= 0; i--) {
				if(max < aoki[i]) {
					max = aoki[i];
					if(yama[i]!=0 && yama[i]!=aoki[i]) {
						System.out.println(0);
						return;
					}
					yama[i] = aoki[i];
				}
			}
		}

		long result = 1;
		for(int i = 0; i < n; i++) {
			if(yama[i]==0) {
				result *= (long)Math.min(aoki[i],taka[i]);
				result %= 1000000007L;
			}
		}

		System.out.println(result);
	}
}