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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
	return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
    public static void AssertEquals<T>(
				       T expected,
				       T actual,
				       [CallerLineNumber] int lno = 0
				       )
	where T : IComparable
    {
	if (expected.CompareTo(actual) != 0)
	{
	    WriteLine($"Assertion Error at line {lno}:");
	    WriteLine($"\texpected: {expected}");
	    WriteLine($"\t  actual: {actual}");
	    Environment.Exit(1);
	}
    }
}

class Program
{
    public static void Main()
    {
	const int M = 1000000007;
	int n = int.Parse(ReadLine());
	int[] t = ReadIntArray();
	int[] a = ReadIntArray();

	int curr = 0;
	for (int i = 0; i < n; i++)
	{
	    int h = t[i];
	    if (h <= curr)
	    {
		AssertEquals(curr, h);
		t[i] *= -1;
	    }
	    curr = h;
	}

	curr = 0;
	for (int i = n-1; i >= 0; i--)
	{
	    int h = a[i];
	    if (h > curr)
	    {
		if (t[i] < 0)
		{
		    t[i] = a[i];
		}
		else if (t[i] != a[i])
		{
		    WriteLine(0);
		    return;
		}
		curr = h;
	    }
	    else
	    {
		if (t[i] < 0)
		{
		    t[i] = -Math.Min(-t[i], h);
		}
	    }
	}

	long ans = 1;
	for (int i = 0; i < n; i++)
	{
	    int h = t[i];
	    if (h < 0)
	    {
		ans = ans * (-h) % M;
	    }
	}

	WriteLine(ans);
    }
}