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 <iostream>
using namespace std;
int main(){
  long long int N, mod = 1000000007;
  cin >> N;
  long long int T[N], A[N];
  for(int i = 0; i < N; ++i)
    cin >> T[i];
  for(int i = 0; i < N; ++i)
    cin >> A[i];
  long long int H[N], L[N];
  fill(H,H+N,100000000000);
  fill(L,L+N,1);
  H[0] = T[0];
  L[0] = T[0];
  L[N-1] = A[N-1];
  H[N-1] = A[N-1];
  if(T[0] > A[0] || T[N-1] < A[N-1]){
    cout << 0 << endl;
    return 0;
  }
  for(int i = 1; i < N; ++i){
    if(T[i-1] != T[i]){
      H[i] = T[i];
      L[i] = T[i];
    }else{
      H[i] = min(H[i],T[i]);
    }
  }
  for(int i = N-2; i >= 0; --i){
    if(A[i+1] != A[i]){
      if((H[i] < A[i] || L[i] > A[i])){
	cout << 0 << endl;
	return 0;
      }
      H[i] = A[i];
      L[i] = A[i];
    }else{
      H[i] = min(H[i],A[i]);
    }
  }
  /*
  for(int i = 0; i < N; ++i){
    cout << H[i] << " ";
  }cout << endl;
  for(int i = 0; i < N; ++i){
    cout << L[i] << " ";
  }cout << endl;
  */
  long long int ans = 1LL;
  for(int i = 0; i < N; ++i){
    ans *= (H[i]-L[i]+1)%mod;
    ans %= mod;
  }
  cout << ans%mod << endl;
  return 0;
}