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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.Numerics;




	class contest
	{
				
		
		static void Main(string[] args)
		{

		  
var n = int.Parse(Console.ReadLine());
            var L = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();            
            var R = Console.ReadLine().Split(' ').Select(int.Parse).ToList();

            var arr = new int[n];
            var arL = new int[n];
            var arR = new int[n];
            var check = new bool[n];



            var set = new HashSet<int>();

            int mxL = 0;
            int mxR = 0;
            for(int i = 0; i < n; i++)
            {
                if (L[i] > mxL)
                {
                    arr[i] = L[i];
                    arL[i] = L[i];
                    mxL = L[i];
                    check[i] = true;
                }
               

                if (R[n - 1 - i] > mxR)
                {
                    arr[n - 1 - i] = R[n - i - 1];
                    arR[n - 1 - i] = R[n - 1 - i];
                    mxR = R[n - i - 1];
                    check[n-1-i] = true;
                }

                if (!check[i]) set.Add(i);
            }
            

            bool ok = true;
            for(int i=0; i< n; i++)
            {
               

                if (arL[i] > 0 && L[i] > R[i])
                {
                    
                        ok = false;
                        break;
                    
                }
                else if (arR[i] > 0 && R[i] > L[i])
                {
                   
                        ok = false;
                        break;
                   
                }
            }
           

            if (!ok) Console.WriteLine(0);
            else if (n == 1)
            {
                if (L[0] == R[0]) Console.WriteLine(1);
                else Console.WriteLine(0);
            }            
            else
            {
                BigInteger count = 1;
                


                int tmp = 0;

                var memo = new int[2];



                
                //var dic = new Dictionary<long, int>();

  
               
                    
                    memo = new int[2];
                    //for (int i = 0; i < n - 1; i++)
                    //{
                    foreach(int i in set)
                { 
                    //if (check[i]) continue;
                    
                    tmp++;
                        if( arr[i-1]>0 && memo[0]==0)
                        {
                            memo[0] = arr[i-1];
                        }

                        if ( arr[i+1]>0)
                        {
                            memo[1] = arr[i + 1];

                        BigInteger mm = Math.Min(memo[0], memo[1]);
                       

                        count *= BigInteger.Pow(mm, tmp);
                        tmp = 0;
                        memo = new int[2];


                    }

                        
                      
                    }


               

                long mod = 1000000007;
                count %= mod;



                Console.WriteLine(count);
            }



            



		
        }
		
		
			
	}