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
MOD = 10 ** 9 + 7
n = int(input())
tlst = list(map(int, input().split()))
alst = list(map(int, input().split()))
cand_t = [[1, 1] for _ in range(n)]
cand_t[0] = [tlst[0], tlst[0]]
for i in range(1, n):
    if tlst[i] == tlst[i - 1]:
        cand_t[i][1] = tlst[i]
    else:
        cand_t[i] = [tlst[i], tlst[i]]
cand_a = [[1, 1] for _ in range(n)]
cand_a[-1] = [alst[-1], alst[-1]]
for i in range(n - 2, -1, -1):
    if alst[i] == alst[i + 1]:
        cand_a[i][1] = alst[i]
    else:
        cand_a[i] = [alst[i], alst[i]]
ans = 1
for (t_r, t_h), (a_r, a_h) in zip(cand_t, cand_a):
    r = max(t_r, a_r)
    h = min(t_h, a_h)
    if r > h:
        print(0)
        break
    ans *= (h - r + 1)
    ans %= MOD
else:
    print(ans)