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 Ruby (2.3.3) (judge verdict: Wrong Answer)

s = gets.chomp.split(" ").map(&:to_i)
t = gets.chomp.split(" ").map(&:to_i)
a = gets.chomp.split(" ").map(&:to_i)

MOD = 1000000007
tmax = t.max
amax = a.max

if t[-1] != a[0]
p 0
else

# At Pos 0
ct = 1

book = true
book = true if s[0]==1

if s[0]==2
  if t[0]==a[0] || t[1] == a[1]
  book = true 
  else
  book = false
  end
end

for i in 1..(s[0]-2)
  if t[i] ==a[i] && (t[i] != tmax || a[i] != amax)
    book = false 
  elsif t[i-1] < t[i] || a[i] > a[i+1]
  elsif t[i-1] > t[i] || a[i] < a[i+1]
    book = false
    #min = t[i]#(t[i]<a[i]) ? t[i] : a[i]
    #ct = (ct *,i min) % MOD
  elsif t[i-1] == t[i] && a[i] == a[i+1]
    min = (t[i]<a[i]) ? t[i] : a[i]
    ct = (ct * min) % MOD
  else
    raise
    #p i
  end

end

if book
  p ct % MOD
else
  p 0
end


end