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;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());//int.Parseは文字列を整数に変換。
		long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
    long[] numsSub = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
    long[] numMemos = new long[n];
    long[] numFixes = new long[n];//固定値なら1
    long maxMemo = 0;
    long answer = 1;
    long mod = 1000000007;

    for(long i = 0; i < n; i++)
    {
      if(nums[i] > maxMemo)
      {
        maxMemo = nums[i];
        numFixes[i] = 1;
      }
      numMemos[i] = nums[i];
    }

    maxMemo = 0;

    for(long i = 0; i < n; i++)
    {
    long memo = n-1-i;
      if(numsSub[memo] > maxMemo)
      {
        maxMemo = numsSub[memo];
        if(numFixes[memo] == 1 && numMemos[memo] != maxMemo ||
          numMemos[memo] < maxMemo) answer = 0;//不正なデータがある
      }else
      {
        if(numFixes[memo] == 1 && numMemos[memo] > maxMemo) answer = 0;//不正なデータがある
        if(numFixes[memo] != 1)
        {
          answer *= Math.Min(maxMemo, numMemos[memo]);
          //Console.WriteLine(maxMemo+" "+ numMemos[memo]);
          answer %= mod;
        }
      }
      //Console.WriteLine(answer);
    }
    
		Console.WriteLine(answer);//WriteLineをWriteとすると、改行なしで出力。
	}
}