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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# def makelist(n, m):
# 	return [[0 for i in range(m)] for j in range(n)]

# n = int(input())
# a, b = map(int, input().split())
# s = input()


n = int(input())
Tmax = list(map(int, input().split()))
Amax = list(map(int, input().split()))

Tmin = [0]*n
Amin = [0]*n

sto = Tmax[0]
Tmin[0] = Tmax[0]
for i in range(1, n):
	if i == n:
		Tmin[i] == Tmax[i]
	elif Tmax[i] == sto:
		Tmin[i] = Tmax[i]
	else:
		if Tmax[i+1] == Tmax[i]:
			Tmin[i] = sto
		else:
			sto = Tmax[i]
			Tmin = Tmax[i]

sto = Amax[-1]
Amin[-1] = Amax[-1]
for i in reversed(range(-n, -1)):
	if i == -n:
		Amin[-n] == Amax[-n]
	elif Amax[i] == sto:
		Amin[i] = Amax[i]
	else:
		if Amax[i-1] == Amax[i]:
			Amin[i] = sto
		else:
			sto = Amax[i]
			Amin = Amax[i]

sa = [0]*n
for i in range(n):
	maxi = min(Tmax[i], Amax[i])
	mini = max(Tmin[i], Amin[i])

	sa[i] = (maxi, mini)

if Tmax[-1] != Amax[-1]:
	print(0)
else:
	ans = 1
	for i in range(n):
		now = sa[i]
		if now[1] > now[0]:
			ans = 0
			break
		else:
			ans *= (now[0] - now[1] + 1)
	print(ans)