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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
 
using namespace std;
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
int main(){
    long long ans=1;
int N,a=0,b=0;
cin >>N;
vector <int>T(N);
vector <int>A(N);
vector <int>TT(N);
vector <int>AA(N);
vector <int>AT(N);
for(int i=0;i<N;i++){
    cin >>T[i];
  
}
for(int i=0;i<N;i++){
    cin >>A[i];
  
}
reverse(A.begin(), A.end());
for(int i=0;i<N;i++){
   if(i==0)TT[i]=1;
   else if(T[i-1]<T[i]){TT[i]=1;
   if(T[i]>A[i])ans=0;
   }
   else TT[i]=T[i];
}
for(int i=0;i<N;i++){
   if(i==0)AA[i]=1;
   else if(A[i-1]<A[i]){AA[i]=1;
 if(A[i]>T[i])ans=0;
   }
   else AA[i]=A[i];
}
reverse(AA.begin(), AA.end());
for(int i=0;i<N;i++){
    AT[i]=min(TT[i],AA[i]);
}
for(int i=0;i<N;i++){
    ans*=AT[i];
    ans%=1000000007;
}

cout <<ans;
}