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;
#define rep1(i,n) for(int i=1;i<=n;++i)
typedef long long ll;
struct Mnt{
	ll t,a;
	bool det;
};

int main(void){
	int N;
	ll res=1;
	cin>>N;
	vector<Mnt> m(N+2);
	m[0].t=m[N+1].t=0;
	rep1(i,N){
		cin>>m[i].t;
		m[i].det=(m[i-1].t!=m[i].t);
	}
	rep1(i,N)cin>>m[i].a;
	bool NG=false;
	for(int i=N;i>0;i--){
		bool det=(m[i].a!=m[i+1].a);
		if(m[i].det){
			if(m[i].t>m[i].a)NG=true;
			if(det && m[i].t!=m[i].a)NG=true;
			//else-> *1
		}
		if(det && m[i].t<m[i].a)NG=true;
		if(NG){
			res=0;
			break;
		}
		if(!det && !m[i].det){
			res*=min(m[i].t,m[i].a);
			res%=1000000007;
		}
	}
	cout<<res<<endl;
	return 0;
}
