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: Accepted)

#include <iostream>
#include <fstream>
#include <set>
#include <map>
#include <string>
#include <vector>
#include <bitset>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <cassert>
#include <queue>

#define mp make_pair
#define pb push_back


typedef long long ll;
typedef long double ld;

using namespace std;


int n;
int gl[120000];
int gr[120000];
int a[120000];
int mx[120000];
int main() {
	cin >> n;
	for (int i = 0; i < n; ++i)
		cin >> gl[i];
	for (int i = 0; i < n; ++i)
		cin >> gr[i];
	int pr = 0;
	for (int i = 0; i < n; ++i) {
		mx[i] = gl[i];
		if (gl[i] > pr) {
			pr = gl[i];
			a[i] = gl[i];
		}
	}
	pr = 0;
	for (int i = n - 1; i >= 0; --i) {
		mx[i] = min(mx[i], gr[i]);
		if (gr[i] > pr) {
			pr = gr[i];
			if (a[i] != 0) {
				if (a[i] != gr[i]) {
					cout << 0 << "\n";
					return 0;
				}
			}
			a[i] = gr[i];
		}
	}
	for (int i = 0; i < n; ++i)
		if (a[i] > mx[i]) {
			cout << 0 << "\n";
			return 0;
		}
	ll ans = 1;
	for (int i = 0; i < n; ++i) {
		if (a[i] == 0)
			ans = (ans * mx[i]) % (ll)(1e9 + 7);
	}
	cout << ans << "\n";
	return 0;
}