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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
T = list(map(int,input().split()))
A = list(map(int,input().split()))
exact = [0] * N # 高さが確定した場所
seem = [0] * N # 高さが確定しない場所のあり得る最大値

cur = 0
for i in range(len(T)):
  if cur < T[i]:
    exact[i] = T[i]
    cur = T[i]
  else:
    seem[i] = cur
    
cur = 0
for i in range(len(A)-1,-1,-1):
  if cur < A[i]:
    if exact[i] != 0 and exact[i] != A[i]: # 既に記録された確定数値が今回の値と異なる場合
      print(0)
      exit(0)
    exact[i] = A[i]
    cur = A[i]
  else:
    seem[i] = min(seem[i],cur)
    
DIV = 10 ** 9 + 7
ans = 1
for i in range(N):
  if exact[i] != 0: # 確定数値があれば場合の数は変わらない
    continue
  else:
    ans *= seem[i]
    ans %= DIV

print(ans)