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.

Examples

Input

5
1 3 3 3 3
3 3 2 2 2


Output

4


Input

5
1 1 1 2 2
3 2 1 1 1


Output

0


Input

10
1 3776 3776 8848 8848 8848 8848 8848 8848 8848
8848 8848 8848 8848 8848 8848 8848 8848 3776 5


Output

884111967


Input

1
17
17


Output

1
#include<bits/stdc++.h>
using namespace std;
typedef long long int LL;
LL n,large=1000000007;
LL f(vector<LL>&d1,vector<LL>&d2){
if(d1.back()!=d2[0])return 0;
LL res=1;
for(LL i=1;i<n-1;i++){
LL tmp=0;
if(d1[i]>d1[i-1])tmp=1;
else tmp=d1[i];
if(d2[i]>d2[i+1]){if(tmp==1&&d2[i]!=d1[i])return 0;else if(d2[i]>d1[i]) return 0;tmp=1;}
else if(tmp==1&&d1[i]>d2[i])return 0;
else if(tmp!=1)tmp=min(tmp,d2[i]);
res=(res*tmp)%large;
}
return res;
}
int main(){
   while(cin>>n){
   vector<LL>d1(n),d2(n);
   for(int i=0;i<n;i++)cin>>d1[i];
   for(int i=0;i<n;i++)cin>>d2[i];
   cout<<f(d1,d2)<<endl;
}
    
}