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.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
 
class Program{
    static void Main(){
        int n = int.Parse(Console.ReadLine());
        int[] T = Console.ReadLine().Split(' ')
                                         .Select(val => int.Parse(val))
                                         .ToArray();
        int[] A = Console.ReadLine().Split(' ')
                                         .Select(val => int.Parse(val))
                                         .ToArray();
        int[] dT = new int[n];
        List<int> iT = new List<int>();
        int[] dA = new int[n];
        List<int> iA = new List<int>();
        for (int i = 0; i < n; i++)
        {
            if(i == 0){
                dT[i] = T[i];
                iT.Add(i);
            }
            else if(i == n - 1){
                dA[i] = A[i];
                iA.Add(i);
            }
            else{
                if(T[i - 1] != T[i]){
                    dT[i] = T[i];
                    iT.Add(i);
                }
                if(A[i] != A[i + 1]){
                    dA[i] = A[i];
                    iA.Add(i);
                }
            }
        }
        Console.Error.WriteLine("iT: {0}", string.Join(" ", iT));
        Console.Error.WriteLine("iA: {0}", string.Join(" ", iA));
        bool contra = false;
        foreach (int idx in iT)
        {
            Console.Error.WriteLine("T idx: {0}", idx);
            if(dT[idx] > A[idx] || (dA[idx] != 0 && dT[idx] != dA[idx])) contra = true;
            if(contra) break;
        }
        foreach (int idx in iA)
        {
            Console.Error.WriteLine("A idx: {0}", idx);
            if(dT[idx] != 0){
                if(dA[idx] > T[idx] || dT[idx] != dA[idx]) contra = true;
            }
            else {
                iT.Add(idx);
                dT[idx] = 1;
            }
            if(contra) break;
            
        }
        Console.Error.WriteLine("iT + iA: {0}", string.Join(" ", iT));
        long pat = 1;
        if(!contra){
            for(int i = 0; i < n; i++){
                if(dT[i] != 0) continue;
                else pat *= T[i] <= A[i] ? T[i] : A[i];
                pat %= (long)Math.Pow(10, 9) + 7;
                Console.Error.WriteLine("i:{0} pat:{1}", i, pat);
            }
        }
        else pat = 0;
        Console.WriteLine(pat);

    }
}