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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
	int mod=1000000000+7;
	
	public static void main(String[] args) {
		new Main().solve();
	}
	
	void solve() {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[]t=new int[n];
		int[]a=new int[n];
		for(int i=0;i<n;i++) {
			t[i]=sc.nextInt();
		}
		for(int i=0;i<n;i++) {
			a[i]=sc.nextInt();
		}
		boolean[] fixed_T=new boolean[n];
		boolean[] fixed_A=new boolean[n];
		fixed_T[0]=true;
		fixed_A[n-1]=true;
		for(int i=0;i<n-1;i++) {
			if(t[i+1]>t[i])fixed_T[i+1]=true;
			else if(t[i+1]==t[i])continue;
			else {
				System.out.println(0);
				return;
			}
		}
		for(int i=n-1;i>0;i--) {
			if(a[i]<a[i-1])fixed_A[i-1]=true;
			else if(a[i]==a[i-1])continue;
			else {
				System.out.println(0);
				return;
			}
		}
		int unfixedCount=0;
		int start=0;
		int end=0;
		long ans=1;
		for(int i=0;i<n;i++) {
			if(!fixed_T[i] && !fixed_A[i]) {
				start=i;
				unfixedCount++;
			}else if(unfixedCount>0){
				end=i;
				int limit=Math.min(t[start-1], a[end]);
				ans*=calc_pow(limit, unfixedCount)%mod;
				ans%=mod;
				unfixedCount=0;
			}else if(fixed_T[i] && fixed_A[i]) {
				if(t[i]==a[i])continue;
				else {
					System.out.println(0);
					return;
				}
			}
		}
		System.out.println(ans);
		
	}
	long calc_pow(long a,long b) {
		long ans=1;
		for(int i=0;i<b;i++) {
			ans*=a%mod;
			ans%=mod;
		}
		return ans%mod;
	}
	
}