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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
        int t[];
        t = new int[n];
        int a[];
        a = new int[n];
        int maxt = 0;
        int maxa = 0;
        int mint = 0;
        int mina = 0;
        int answer = 0;
        int c[];
        c = new int[n];
        for(int i = 0; i<n; i++){
		t[i] = sc.nextInt();
            if(maxt < t[i]){
                maxt = t[i];
            }
            else if(mint > t[i]){
                mint = t[i];
            }
            if(i>0 && t[i] != t[i-1]){
                c[i] = t[i];
            }
            else{
                c[i] = 0;
            }
        }
        int cc = 1;
        boolean er = false;
        for(int i = 0; i<n; i++){
		a[i] = sc.nextInt();
            if(maxa < a[i]){
                maxa = a[i];
            }
            else if(mina > a[i]){
                mina = a[i];
            }
            if(i>0 && a[i] != a[i-1]){
                if(c[i-1] == 0){
                    c[i-1] = a[i-1];
                }
                else if(c[i-1] != a[i-1]){
                    er = true;
                }
            }
        }
        for(int i=0; i<c.length; i++){
            if(c[i] == 0){
                if(t[i]>a[i]){
                    cc = cc * a[i];
                }
                else{
                    cc = cc * t[i];
                }
            }
        }
        if(maxa != maxt || er){
            System.out.println(answer);
        }
        else{
            answer = cc % (10^9 + 7);
            System.out.println(answer);
        }
	}
}