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 + 2];
		int[] A = new int[N + 2];
		for (int i = 1; i <= N; i++) {
			T[i] = sc.nextInt();
		}
		for (int i = 1; i <= N; i++) {
			A[i] = sc.nextInt();
		}
		sc.close();

		boolean wrong = false;
		int[] min = new int[N + 1];
		int[] max = new int[N + 1];

		for (int i = 1; i <= N; i++) {
			if (T[i] > T[i - 1]) {
				max[i] = T[i];
				min[i] = T[i];
			} else {
				max[i] = max[i - 1];
				min[i] = 1;
			}
		}
		for (int i = N; i >= 1; i--) {
			if (A[i] > A[i + 1]) {
				if (max[i] >= A[i] && A[i] >= min[i]) {
					max[i] = A[i];
					min[i] = A[i];
				} else {
					wrong = true;
					break;
				}
			} else {
				if (A[i] < min[i]) {
					wrong = true;
					break;
				} else {
					max[i] = Math.min(A[i], max[i]);
				}
			}
		}
		long ans = 1;
		long P = 1000000007;
		if (wrong == false) {
			for (int i = 1; i <= N; i++) {
				long a = max[i] - min[i] + 1;
				ans = (ans * a) % P;
			}
		} else {
			ans = 0;
		}
		System.out.println(ans);
	}
}