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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int MAX_N = 100005;
const ll MOD = 1e9+7;
ll T[MAX_N],A[MAX_N];

int main()
{
	int N;
	cin >> N;
	rep(i,N)
	{
		cin >> T[i];
	}
	rep(i,N)
	{
		cin >> A[i];
	}

	ll ans = 1;
	if (A[0] < T[0])
	{
		cout << 0 << endl;
		return 0;
	}
	for(int i = 1; i < N-1; ++i)
	{
		bool flag1 = false, flag2 = false;
		if (T[i-1] < T[i])
		{
			flag1 = true;
		}
		if (A[i] > A[i+1])
		{
			flag2 = true;
		}

		if (flag1 && flag2)
		{
			if (T[i] != A[i])
			{
				cout << 0 << endl;
				return 0;
			}
		}
		else if (flag1 && !flag2)
		{
			if (A[i] < T[i])
			{
				cout << 0 << endl;
				return 0;
			}
		}
		else if (!flag1 && flag2)
		{
			if (T[i] < A[i])
			{
				cout << 0 << endl;
				return 0;
			}
		}
		else
		{
			ans = ans * min(T[i],A[i]) % MOD;
		}
	}
	if (T[N-1] < A[N-1])
	{
		cout << 0 << endl;
		return 0;
	}
	cout << ans << endl;
	return 0;
}