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<cmath>
#include<string.h>
#include<stdio.h>
#include<algorithm>
using namespace std;

int n;
int a[100011],b[100011];
int h[100011];
int ll[100011],rr[100011];

long long MOD=1000000007;
long long ans;

int main()
{
    int i,j;
    bool gg=0;
    scanf("%d",&n);
    for(i=1;i<=n;i++)
    {
        scanf("%d",&a[i]);
    }
    for(i=1;i<=n;i++)
    {
        scanf("%d",&b[i]);
    }
    a[0]=b[n+1]=-1;
    
    memset(h,-1,sizeof(h));
    for(i=1;i<=n;i++)
    {
        if(a[i]!=a[i-1])
        {
            h[i]=a[i];
        }
    }
    for(i=n;i>=1;i--)
    {
        if(b[i]!=b[i+1])
        {
            if(h[i]==-1 || h[i]==b[i])
            {
                h[i]=b[i];
            }
            else
            {
                gg=1;
            }
        }
    }
    
    if(gg==1)
    {
        cout<<0<<endl;
    }
    else
    {
        ans=1;
        ll[0]=rr[n+1]=0;
        for(i=1;i<=n;i++)
        {
            if(h[i]!=-1)
            {
                ll[i]=h[i];
            }
            else
            {
                ll[i]=ll[i-1];
            }
        }
        
        for(i=n;i>=1;i--)
        {
            if(h[i]!=-1)
            {
                rr[i]=h[i];
            }
            else
            {
                rr[i]=rr[i+1];
            }
        }
        
        for(i=1;i<=n;i++)
        {
            if(h[i]==-1)
            {
                ans=ans*min(ll[i],rr[i])%MOD;
            }
        }
        
        cout<<ans<<endl;
    }
    
    
    
    
    return 0;
}