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: Time Limit Exceeded)

import sys
n = int(input())
t_list = list(map(lambda number: int(number), input().split(' ')))
a_list = list(map(lambda number: int(number), input().split(' ')))


def fail():
    print(0)
    sys.exit()

if t_list[-1] != a_list[0]:
    fail()

candidates = []
for i in range(n):
    if i == 0:
        candidates.append([t_list[i]])
    elif i == n - 1:
        candidates.append([a_list[i]])
    else:
        if t_list[i] != t_list[i - 1] and a_list[i] != a_list[i + 1]:
            if t_list[i] == a_list[i]:
                candidates.append([t_list[i]])
            else:
                fail()
        elif t_list[i] != t_list[i - 1]:
            if t_list[i] <= a_list[i]:
                candidates.append([t_list[i]])
            else:
                fail()
        elif a_list[i] != a_list[i + 1]:
            if a_list[i] <= t_list[i]:
                candidates.append([a_list[i]])
            else:
                fail()
        else:
            candidates.append([1, min(t_list[i], a_list[i])])


result = 1

for c in candidates:
    if len(c) == 1:
        continue
    else:
        partial = c[1] % (10**9 + 7)
        if partial == 0:
            print(0)
            sys.exit()
        else:
            result *= partial
print(result % (10**9 + 7))