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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

#define MAX(x,y) (((x)<(y))?(y):(x))

typedef long long ll;

int main(void){
  ll t[100000],a[100000];
  ll maxT,maxA,mtp,map,tM=1,aM=1;
  int N,i,j,k;
  ll const mod=(ll)1E9+7;

  scanf("%d",&N);
  for(i=0;i<N;i++) scanf("%lld",&t[i]);
  for(i=0;i<N;i++) scanf("%lld",&a[i]);
  for(i=maxT=maxA=0;i<N;i++){
    if(maxT<t[i]) maxT=t[mtp=i];
    if(maxA<a[N-1-i]) maxA=a[map=N-1-i];
  }
  if(maxT!=maxA && t[mtp]!=a[mtp] && t[map]!=a[map]){
    puts("0");
    return 0;
  }

  for(i=1;i<N && t[i]!=maxT;i++){
    if(t[i]==t[i-1]){
      tM*=t[i-1];
      tM%=mod;
    }else if(t[i]<t[i-1]){
      puts("0");
      return 0;
    }
  }

  for(j=N-1;j>i;j--){
    if(a[j]<=a[j+1]){
      aM*=a[j+1];
      aM%=mod;
    }else if(a[j]>a[j+1]){
      puts("0");
      return 0;
    }
  }

  printf("%lld\n",aM*tM%mod);
  
  return 0;
}