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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using static System.Console;
using static System.Math;
class E { static void Main() => new K(); }
class K
{
	int F() => int.Parse(ReadLine());
	int[] G() => ReadLine().Split().Select(x => int.Parse(x)).ToArray();
	const long Mod = 1000000007;
	int N;
	int[] A, B, M;
	bool[] X;
	public K()
	{
		N = F();
		A = G();
		B = G();
		M = new int[N];
		X = new bool[N];
		WriteLine(Calc());
	}
	long Calc()
	{
		for (var i = 0; i < N; i++) if (!H(i)) return 0;
		var a = 1L;
		for (var i = 0; i < N; i++) if (!X[i]) a = (a * M[i]) % Mod;
		return a;
	}
	bool H(int n)
	{
		var l = -1;
		if (n == 0 || A[n - 1] < A[n]) l = A[n];
		var r = -1;
		if (n == N - 1 || B[n] > B[n + 1]) r = B[n];
		if (l < 0 && r < 0)
		{
			M[n] = Min(A[n], B[n]);
			return true;
		}
		X[n] = true;
		if (l < 0) return r <= A[n];
		else if (r < 0) return l <= B[n];
		else return l == r;
	}
}