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<vector>
#include<algorithm>
using namespace std;

int main()
{
	long long ans = 1;

	int n;
	cin >> n;
	vector<int> th(n), ao(n);
	for (int i = 0; i < n; ++i) cin >> th[i];
	for (int i = 0; i < n; ++i) cin >> ao[i];

	auto tmax = max_element(th.begin(), th.end());
	auto amax = max_element(ao.begin(), ao.end());
	if (*tmax != *amax)
	{
		cout << "0" << endl;
		exit(0);
	}
	vector<int> left(n), right(n); //確定した要素
	int tool = 0; //vector管理
	//高橋のを元に左から確定
	int work = 0;
	for (int i = 0; i < n; ++i)
	{
		if (work < th[i])
		{
			work = th[i];
			left[tool++] = i;
		}
	}

	/*
	cout << "size=" << left.size() << " ";
	for (int i : left) cout << i << " ";
	cout << endl;
	*/
	//今度は右から
	work = 0;
	tool = 0;
	for (int i = n - 1; i >= 0; --i)
	{
		if (work < ao[i])
		{
			work = ao[i];
			right[tool++] = i;
		}
	}
	/*
	cout << "size=" << right.size() << " ";
	for (int i : right) cout << i << " ";
	cout << endl;	
	*/
	tool = 0;
	vector<int> merge(n*2); //leftとrightを結合
	for (int i = 0; i < left.size(); ++i) merge[tool++] = left[i];
	for (unsigned int i = 0; i < right.size(); ++i)
	{
		if (find(merge.begin(),merge.end(), right[i]) == merge.end())
		{
			merge[tool++] = right[i];
			//merge.push_back(right[i]);
		}
	}

	for (int i = 0; i < n; ++i)
	{
		if (find(merge.begin(), merge.end(), i) != merge.end())
		{
			continue;
		}
		else
		{
			if (th[i]>ao[i])
			{
				ans = ans % (long long)(pow(10, 9) + 7);
				ans *= ao[i];
			}
			else
			{
				ans = ans % (long long)(pow(10, 9) + 7);
				ans *= th[i];
			}
		}
	}
	cout << ans % (long long)(pow(10,9)+7) << endl;

	//for (int i : merge) cout << i << " ";

	//cout << endl << (8848 * 8848 * 8848) % (1000000007) << endl;
	return 0;
}