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.*;

public class Main {

    static final long mod = 1_000_000_007;
    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];
        for (int i = 0; i < n; i++) {
            t[i] = sc.nextInt();
        }
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        int[] max = new int[n];
        Arrays.fill(max, Integer.MAX_VALUE);
        int[] d = new int[n];
        Arrays.fill(d, -1);
        d[0] = max[0] = t[0];
        d[n-1] = max[n-1] = a[n-1];
        for (int i = 1; i < n; i++) {
            if(t[i-1] < t[i]) d[i] = max[i] = t[i];
            else max[i] = t[i];
        }
        boolean able = true;
        for (int i = n-2; i >= 0; i--) {
            if(a[i+1] < a[i]){
                if(d[i] != -1 && d[i] != a[i]){
                    able = false;
                    break;
                }
                d[i] = max[i] = a[i];
            }else{
                if(a[i] < max[i]) max[i] = a[i];
            }
        }
        long ans = 1L;
        if(able){
            for (int i = 0; i < n; i++) {
                if(d[i] < 0){
                    ans = (ans * max[i]) % mod;
                }
            }
        }else ans = 0;
        System.out.println(ans);
        sc.close();

    }

}