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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>

int main(void){
    int n;
    scanf("%d",&n);
    bool truth=true;
    long long t[n],a[n],m[n],ans=1,max=0;
    for (int i=0; i<n; i++){
        scanf("%lld",&t[i]);

    }
    
    for (int i=0; i<n; i++){
        scanf("%lld",&a[i]);
    }
    
    for (int i=0; i<n; i++){
        if (t[i]<=a[i]){
            m[i]=t[i];
        } else {
            m[i]=a[i];
        }
    }
    for (int i=0; i<n; i++){
        if (m[i]>max){
            max=m[i];
        }
        if (max<t[i]){
            truth=false;
        }
    }
    max=0;
    for (int i=n-1; i>=0; i--){
        if (m[i]>max){
            max=m[i];
        }
        if (max<a[i]){
            truth=false;
        }
    }
    
    bool climb=false;
    for (int i=0; i<n; i++){
        if (climb==false){
            if (m[i]==m[i-1]){
                ans=ans*m[i]%1000000007;
            }
        } else {
            if (m[i]==m[i+1])
                ans=ans*m[i]%1000000007;
            
        }
        if (m[i]==max){
            climb=true;
        }
    }
    
    if (truth==false){
        ans=0;
    }
    printf("%lld\n",ans);
	return 0 ;
}