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 M = 1e9 + 7;
int main() {
    ll 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];
    }
    ll maxl = max_element(T.begin(), T.end()) - T.begin();
    reverse(A.begin(), A.end());
    ll maxr = max_element(A.begin(), A.end()) - A.begin();
    maxr = N - 1 - maxr;
    reverse(A.begin(), A.end());

    bool flag = true;
    if (maxl > maxr) {
        flag = false;
    }
    if (T[N - 1] != A[0]) {
        flag = false;
    }

    ll sum = 1;
    for (int i = 1; i < maxl; i++) {
        if (T[i] == T[i - 1]) {
            sum *= T[i];
            sum %= M;
        }
    }
    for (int i = N - 2; i > maxr; i--) {
        if (A[i] == A[i + 1]) {
            sum *= A[i];
            sum %= M;
        }
    }

    ll gap = maxr - maxl - 1;
    while (gap > 0) {
        sum *= T[N - 1];
        sum %= M;
        gap--;
    }

    cout << (flag ? sum : 0) << endl;
}