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 <iostream>
#include <string>
#include <cstdlib>
#include <cstdio>
#include <queue>
#include <stack>
#include <list>
#include <utility>
#include <vector>
#include <set>
#include <algorithm>
#include <cmath>
#include <climits>
#include <map>
#include <unordered_map>
#include <string.h>
#include<iomanip>
#include <iterator>
#include <locale>

#define all(a) a.begin(),a.end()
#define VV(T) vector<vector< T > >
#define rep(i,N) for(int i = 0; i <N; i++)
#define repsg(i,s,g) for(int i = s; i <g; i++)
#define name(x) #x


using namespace std;

const int INF = INT_MAX;
const long long INFL = 1LL<<40;
const double PI = atan(1)*4;
const long long MOD = pow(10,9)+7;
int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

typedef long long ll,LL;
typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;
typedef pair<int,int> pii;
typedef pair<LL, LL> pLL;


// vector入力
template<typename T>
istream& operator >> (istream& is, vector<T>& vec){
    for(T& x: vec) is >> x;
    return is;
}
// vector出力
template<typename T>
ostream& operator << (ostream& os, vector<T>& vec){
    for(int i=0; i<vec.size(); i++){
        os << vec[i] << ( i+1 == vec.size() ? "" : " " );
    }
    return os;
}


int main() {
    int n;cin>>n;
    vector<ll> t(n);cin>>t;
    vector<ll> a(n);cin>>a;

    if(a[0]!=t[n-1]){
        cout<<0<<endl;
        return 0;
    }
    
    ll ans = 1;
    repsg(i,1,n-1){
        /// hiはt[i]以下かつa[i]以下
        if(a[i]>a[i+1] || t[i]>t[i-1] )continue;
        ans *= min(t[i],a[i]);
        ans%=MOD;
    }
    cout<<ans<<endl;
    
    return 0;
}