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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class Program
{
    private int N;
    private int[]T,A;
    private void Scan()
    {
        N=int.Parse(Console.ReadLine());
        T=Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        A=Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    }
    
    public void Solve()
    {
        Scan();
        bool[]flag=new bool[N];
        for(int ti=0;ti<N;ti++)
        {
            int ai=N-1-ti;
            if(ti==0||T[ti-1]<T[ti])
            {
                if(A[ti]>=T[ti])
                {
                    flag[ti]=true;
                }
                else
                {
                    //Console.WriteLine($"{ti}");
                    Console.WriteLine(0);
                    return;
                }
            }
            
            if(ai==N-1||A[ai+1]<A[ai])
            {
                if(T[ai]>=A[ai])
                {
                    flag[ai]=true;
                }
                else
                {
                    //Console.WriteLine($"{ai}");
                    Console.WriteLine(0);
                    return;
                }
            }
        }
        long ans=1;
        for(int i=0;i<N;i++)
        {
            if(flag[i])continue;
            ans*=Math.Min(A[i],T[i]);
            ans%=1000000007;
        }
        Console.WriteLine(ans);
    } 
    
    static void Main()
    {
        new Program().Solve();
    }
}