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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] t = new int[n];
		int[] a = new int[n];
		boolean[] tt = new boolean[n];
		boolean[] aa = new boolean[n];
		for (int i = 0; i < n; i++) {
			t[i] = sc.nextInt();
		}
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		tt[0] = true;
		aa[n - 1] = true;
		for (int i = 1; i < n; i++) {
			if (t[i] > t[i - 1]) {
				tt[i] = true;
			}
		}
		for (int i = n - 2; i >= 0; i--) {
			if (a[i] > a[i + 1]) {
				aa[i] = true;
			}
		}
		long ans = 1;
		int div = 1000000007;
		for (int i = 0; i < n; i++) {
			if (aa[i] && !tt[i]) {
				if (a[i] <= t[i]) {
				} else {
					ans = 0;
					break;
				}
			} else if (!aa[i] && tt[i]) {
				if (a[i] >= t[i]) {
				} else {
					ans = 0;
					break;
				}
			} else if (aa[i] && tt[i]) {
				if (a[i] == t[i]) {
				} else {
					ans = 0;
					break;
				}
			} else if (!aa[i] && !tt[i]) {
				ans = (ans * Math.min(a[i], t[i])) % div;
			}
		}
		System.out.println(ans);
	}
}