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: Accepted)

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const ll MOD = 1e9+7;

int main() {
    int n; cin >> n;
    vector<ll> t(n), a(n);
    for (int i=0; i<n; ++i) {
        cin >> t[i];
    }
    for (int i=0; i<n; ++i) {
        cin >> a[i];
    }
    vector<bool> ft(n);
    ll cur=t[0];
    ft[0]=true;
    for (int i=1; i<n; ++i) {
        if (t[i]!=cur) {
            ft[i]=true;
            cur=t[i];
        }
    }
    vector<bool> fa(n);
    cur=a[n-1];
    fa[n-1]=true;
    for (int i=n-1; i>=0; --i) {
        if (a[i]!=cur) {
            fa[i]=true;
            cur=a[i];
        }
    }
    ll ans=1;
    for (int i=0; i<n; ++i) {
        if (fa[i] && ft[i]) {
            if (a[i]!=t[i]) {
                ans=0;
            }
        } else if (fa[i]) {
            if (a[i]>t[i]) {
                ans=0;
            }
        } else if (ft[i]) {
            if (t[i]>a[i]) {
                ans=0;
            }
        } else {
            ans*=min(a[i], t[i]);
            ans%=MOD;
        }
    }
    cout << ans;
    return 0;
}