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)

MOD = 10**9+7
n = int(input())
T = list(map(int, input().split()))
A = list(map(int, input().split()))
n_cases = [0]*n
n_cases[0] = n_cases[-1] = 1
height = [0]*n
if n == 1 and T[0] != A[-1]:
    print(0)
    exit()
height[0] = T[0]
height[-1] = A[-1]
for i, (t1, t2) in enumerate(zip(T, T[1:]), 1):
    if t1 != t2:
        n_cases[i] = 1
        height[i] = t2
        

for i, (a1, a2) in enumerate(zip(A[::-1], A[::-1][1:]), 2):
    if a1 != a2:
        n_cases[-i] = 1
        if height[-i] == a2 or height[-i] == 0:
            continue
        print(0)
        exit()

for i, (t, a) in enumerate(zip(T, A)):
    if n_cases[i]:
        continue
    n_cases[i] = min(t, a)


ans = 1
for x in n_cases:
    ans *= x
    ans %= MOD
print(ans)