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;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Solve(int N, int[] T, int[] A)
        {
            int[] mins = Enumerable.Repeat(int.MinValue, N).ToArray();
            int[] maxs = Enumerable.Repeat(int.MaxValue, N).ToArray();

            mins[0] = Math.Max(T[0], mins[0]);
            maxs[0] = Math.Min(T[0], maxs[0]);
            for (int i = 1; i < N; ++i)
            {
                if (T[i] > T[i - 1])
                {
                    mins[i] = Math.Max(T[i], mins[i]);
                    maxs[i] = Math.Min(T[i], maxs[i]);
                }
                else if (T[i] == T[i - 1])
                {
                    mins[i] = Math.Max(1, mins[i]);
                    maxs[i] = Math.Min(T[i], maxs[i]);
                }
                else
                {
                    return 0;
                }
            }

            mins[N - 1] = Math.Max(A[N - 1], mins[N - 1]);
            maxs[N - 1] = Math.Min(A[N - 1], maxs[N - 1]);
            for (int i = N - 2; i >= 0; --i)
            {
                if (A[i] > A[i + 1])
                {
                    mins[i] = Math.Max(A[i], mins[i]);
                    maxs[i] = Math.Min(A[i], maxs[i]);
                }
                else if (A[i] == A[i + 1])
                {
                    mins[i] = Math.Max(1, mins[i]);
                    maxs[i] = Math.Min(A[i], maxs[i]);
                }
                else
                {
                    return 0;
                }
            }

            long prod = 1;
            for (int i = 0; i < N; ++i)
            {
                if (mins[i] <= maxs[i])
                {
                    prod *= maxs[i] - mins[i] + 1;
                    prod %= 1000000007;
                }
                else
                {
                    return 0;
                }
            }
            return (int)prod;
        }
        static void Main(string[] args)
        {
            int N = ReadInt();
            int[] T = ReadInts();
            int[] A = ReadInts();
            Console.WriteLine(Solve(N, T, A));
        }
    }
}