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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Solve{
    int N;
    long[] t;
    long[] a;
    public Solve(){}
    public static int Main(){
        new Solve().Calc();
        return 0;
    }
    void Calc(){
        getinput();
        bool[] c = new bool[N];
        long[] d = new long[N];
        long count = 1;
        for(int i=0;i<N;i++){
            c[i] = false;
        }
        d[0] = t[0];
        c[0] = true; 
        for(int i=1;i<N;i++){
            if(t[i] > t[i-1]){
                d[i] = t[i];
                c[i] = true;
            }
        }
        if(c[N-1]){
            if(d[N-1] != a[N-1]){
                Console.WriteLine(0);
                return;
            }
        }
        else{
            c[N-1] = true;
            d[N-1] = a[N-1];
        }
        for(int i=N-2;i>=0;i--){
            if(a[i] > a[i+1]){
                if(c[i]){
                    if(d[i] != a[i]){
                        Console.WriteLine(0);
                        return;
                    }
                }
                else{
                    c[i] = true;
                    d[i] = a[i];
                }
            }
        }
        for(int i=1;i<N-1;i++){
            if(t[i] == t[i-1] && a[i] == a[i+1]){
                long min;
                if(a[i] > t[i]){
                    min = t[i];
                }
                else{
                    min = a[i];
                }
                count = (count*min)%Define.mod;
            }
        }
        Console.WriteLine(0);
    }
    void getinput(){
        string[] str;
        N = int.Parse(Console.ReadLine());
        a = new long[N];
        t = new long[N];
        str = Console.ReadLine().Split(' ');
        for(int i=0;i<N;i++){
            t[i] = Int64.Parse(str[i]);
        }
        str = Console.ReadLine().Split(' ');
        for(int i=0;i<N;i++){
            a[i] = Int64.Parse(str[i]);
        }
    }    
}
public static class Define{
    public const long mod = 1000000007;
}