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<iostream>
#include<algorithm>
#include<string>
using namespace std;
#define ll long long
#define N 100005
#define MOD 1000000007
ll n;
ll T[N], A[N];
ll lot[N], hit[N], loa[N], hia[N];
ll overlap(ll l1, ll h1, ll l2, ll h2){
	if (l1 > h2 || l2 > h1)return 0;
	return min(h1, h2) + 1 - max(l1, l2);
}
int main(){
	cin >> n;
	for (int i = 0; i < n; i++){
		cin >> T[i];
		if (i == 0 || T[i] > T[i - 1]){
			lot[i] = hit[i] = T[i];
		}
		else {
			lot[i] = 1;
			hit[i] = T[i];
		}
	}
	for (int i = 0; i < n; i++){
		cin >> A[i];
	}
	for (int i = n - 1; i >= 0; i--){
		if (i == n - 1 || A[i] > A[i + 1]){
			loa[i] = hia[i] = A[i];
		}
		else {
			loa[i] = 1;
			hia[i] = A[i];
		}
	}
	int ret=1;
	for (int i = 0; i < n; i++){
		ret = (ret*overlap(lot[i], hit[i], loa[i], hia[i]))%MOD;
	}
	cout << ret << endl;
	return 0;
}