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;
using System.Linq;
using static Input;
public class Hello
{
    private const int INF = 1000000007;
    public static void Main()
    {
        int N = NextInt();
        //int N = 100000;
        int[] T = LineInt();
        int[] A = LineInt();
        //int[] T = Enumerable.Repeat(1000000000, N).ToArray();
        //int[] A = Enumerable.Repeat(1000000000, N).ToArray();

        int[] M = new int[N];
        M[0] = T[0];
        M[N - 1] = A[N - 1];
        for (int i = 1; i < N; i++)
            if (T[i - 1] != T[i])
                M[i] = T[i];
        for (int i = 0; i < N - 1; i++)
            if (A[i] != A[i + 1])
            {
                if (M[i] != 0 && M[i] != A[i]) { Console.WriteLine(0); return; }
                else M[i] = A[i];
            }
        //0の場所に何を入れるかによってかわる
        long ans = 1;
        for (int i = 0; i < N; i++)
        {
            if (M[i] != 0)
            {
                if (T[i] < M[i]) { Console.WriteLine(0);return; }
                continue;
            }
            long X = M[i - 1];
            int count = 1;
            while (M[i + count] == 0) count++;
            X = Math.Min(X, M[i + count]);
            for (int j = 0; j < count; j++) { ans *= X; ans %= INF; }
            i += count;
        }
        //M.ToList().ForEach(v => Console.Write(v + " "));
        //Console.WriteLine();
        Console.WriteLine(ans);
    }
}

public class Input
{
    private static Queue<string> queue = new Queue<string>();
    private static void Confirm() { if (queue.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) queue.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(queue.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(queue.Dequeue()); }
    public static string NextString() { Confirm(); return queue.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(queue.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}