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 (2.7.6) (judge verdict: Wrong Answer)

n = int(raw_input())
t = map(int, raw_input().split())
a = map(int, raw_input().split())
mi = [1 for i in range(n)]
ma = [10**9 for i in range(n)]
for i, e in enumerate(t):
    if i == 0:
        mi[i] = e
        ma[i] = e
    else:
        if e > t[i-1]:
            mi[i] = e
            ma[i] = e
        elif e == t[i-1]:
            ma[i] = e
        else:
            print 0
            exit()

a = a[::-1]
mi = mi[::-1]
ma = ma[::-1]

for i, e in enumerate(a):
    if i == 0:
        if mi[i] <= e <= ma[i]:
            mi[i] = e
            ma[i] = e
        else:
            print mi
            print ma
            print 0
            exit()
    else:
        if e > a[i-1]:
            if mi[i] <= e <= ma[i]:
                mi[i] = e
                ma[i] = e
            else:
                print 0
                exit()
        elif e == a[i-1]:
            if mi[i] <= e <= ma[i]:
                ma[i] = e
        else:
            print 0
            exit()
res = 1
for i in range(n):
    res *= ma[i] - mi[i] + 1
    res = res % (10**9+7)
print res % (10**9+7)