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 System.Text;
using System.Threading.Tasks;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] t = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            int[] a = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            int[] h = new int[n];
            bool[] d = new bool[n];
            int result = 1;

            for (int i = 0; i < n; i++)
            {
                h[i] = t[i];
                d[i] = true;
                if (i > 0)
                    if (h[i - 1] >= h[i])
                        d[i] = false;
            }

            for (int i = n - 1; i >= 0; i--)
            {
                if (!d[i])
                {
                    if (h[i] >= a[i])
                    {
                        h[i] = a[i];
                        d[i] = true;
                        if (i < n - 1)
                            if (h[i + 1] >= h[i])
                                d[i] = false;
                    }
                    else
                    {
                        if (i < n - 1)
                        {
                            if (a[i + 1] < a[i])
                            {
                                if (a[i] != h[i])
                                    result = 0;
                            }
                        }
                    }
                }
                else
                {
                    if (i < n - 1)
                    {
                        if (a[i + 1] < a[i])
                        {
                            if (a[i] != h[i])
                                result = 0;
                        }
                    }
                }
            }

            for (int i = 0; i < n; i++)
            {
                if (!d[i])
                {
                    result = (int)(((long)result * h[i]) % 1000000007);
                }
            }

            Console.WriteLine(result);
        }
    }
}