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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] a = new int[N];
		int[] b = new int[N];
		for (int i = 0; i < N; i++) {
			a[i] = sc.nextInt();
		}
		for (int i = 0; i < N; i++) {
			b[i] = sc.nextInt();
		}
		System.out.println(mountainSeqNum(a, b));
	}

	private static long mountainSeqNum(int[] a, int[] b) {
		if(a.length==1) {
			if(a[0]!=b[0]){
				return 0;
			}
		}
		int c[] = new int[a.length];
		int pre = 0;// 上一座
		int zl[] = new int[a.length];
		for (int i = 0; i < a.length; i++) {
			if (a[i] > pre) {
				c[i] = a[i];
				pre = a[i];
			} else {
				zl[i] = pre;
			}
		}
		int behind = 0;// 反序上一座
		for (int i = b.length - 1; i > 0; i--) {
			if (b[i] > behind) {
				if (c[i] == 0) {
					c[i] = b[i];
					behind = b[i];
					zl[i] = 0;
				} else {
					// 存在值
					if (c[i] != b[i]) {// 不等于当前值
						return 0;
					}
				}
			} else {
				if (c[i] == 0) {
					if (zl[i] > behind) {
						zl[i] = behind;
					}
				} else {
					// 存在值时
					if (c[i] > b[i]) {
						return 0;
					}
				}
			}
		}
		long sum = 1;
		for (int i = 0; i < zl.length; i++) {
			if (zl[i] != 0) {
				sum = sum * zl[i];
				if (sum >= 1000000007) {
					sum %= 1000000007;
				}

			}
		}
		return sum;
	}
}