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;
using System.Text.RegularExpressions;

namespace CODEFEST2016C {
    class Program {
        struct Cake {
            public string name;
            public int num;
            public Cake(int i, string str) {
                this.num = i;
                this.name = str;
            }
            public void setNum(int i) {
                num = i;
            }
        }
        static void Main(string[] args) {
            int N = int.Parse(Console.ReadLine());
            List<int> Taka = new List<int>(), Ao = new List<int>();
            string[] TakaStr = Console.ReadLine().Split(' ');
            string[] AoStr = Console.ReadLine().Split(' ');
            foreach(var i in TakaStr) {
                Taka.Add(int.Parse(i));
            }
            foreach(var i in AoStr) {
                Ao.Add(int.Parse(i));
            }
            if(Taka.Max() != Ao.Max()) {
                Console.Write('0');
                return;
            }
            int Ans = 1;
            int TakasMax = 0, AosMax = 0;

            for(int i = 0; i < N; i++) {
                bool GO = true;
                if(TakasMax < Taka[i]) {
                    TakasMax = Taka[i];
                    GO = false;
                } 
                if(AosMax < Ao[i]) {
                    AosMax = Ao[i];
                    GO = false;
                }
                if(GO) {
                    Ans += Minny(Taka[i],Ao[i])-1;
                }
            }
            Console.Write(Ans % (Math.Pow(10, 9) + 7));
        }

        static int Minny(int a, int b) {
            if(a < b)
                return a;
            else
                return b;
        }
    }
}