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: Wrong Answer)

N=int(input())

T=list(map(int,input().split()))
A=list(map(int,input().split()))
for i in range(1,N):
    if T[i]<T[i-1]:
        print(0)
        exit()
    if A[N-1-i]<A[N-i]:
        print(0)
        exit()

if T[N-1]!=A[0]:
    print(0)
else:
    L1=[]
    for i in range(N):
        L1.append(min(T[i],A[i]))
        
    L2=[1]
    Num=L1[0]
    for i in range(1,N):
        if L1[i]==Num:
            L2.append(Num)
        elif L1[i]>Num:
            L2.append(1)
            Num=L1[i]
        else:
            L2.append(L1[i])
    L3=[0 for i in range(N)]
    Num=L1[N-1]
    L3[N-1]=1
    for i in range(1,N):
        if L1[N-1-i]==Num:
            L3[N-1-i]=Num
        elif L1[i]>Num:
            L3[N-1-i]=1
            Num=L1[N-1-i]
        else:
            L3[N-1-i]=L1[N-1-i]
    #print(L2)
    #print(L3)
    L4=[]
    for i in range(N):
        L4.append(min(L2[i],L3[i]))
    #print(L4)
    
    ans=1
    for i in range(N):
        ans*=L4[i]
        ans%=(10**9+7)
    print(ans)