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.

Examples

Input

5
1 3 3 3 3
3 3 2 2 2


Output

4


Input

5
1 1 1 2 2
3 2 1 1 1


Output

0


Input

10
1 3776 3776 8848 8848 8848 8848 8848 8848 8848
8848 8848 8848 8848 8848 8848 8848 8848 3776 5


Output

884111967


Input

1
17
17


Output

1
import sys

def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline

def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N] = [long(input_raw[0])]
    input_rawT = read_func().strip().split()
    input_rawA = read_func().strip().split()
    T = []
    A = []
    for i in range(N):
        T.append(long(input_rawT[i]))
        A.append(long(input_rawA[i]))
    count = 1
    h_T = [(0, 0) for i in range(N)]
    h_A = [(0, 0) for i in range(N)]
    h_T[0] = (T[0], T[0])
    h_A[N - 1] = (A[N - 1], A[N - 1])

    for i in range(1, N):
        j = N - 1 - i
        if T[i] == T[i - 1]:
            h_T[i] = (1, T[i])
        else:
            h_T[i] = (T[i], T[i])

        if A[j] == A[j + 1]:
            h_A[j] = (1, A[j])
        else:
            h_A[j] = (A[j], A[j])

    count = 1L
    for i in range(0, N):
        h1 = max(h_A[i][0], h_T[i][0])
        h2 = min(h_A[i][1], h_T[i][1])
        if h1 > h2:
            print 0
            exit()
        count = ((count * long(h2 - h1 + 1)) % long(1e9 + 7))

    print count




if __name__ == '__main__':
    main()
