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: Accepted)

class Alipnists
  def solve
    n = gets.chomp.to_i
    ts = gets.scan(/\d+/).map(&:to_i)
    as = gets.scan(/\d+/).map(&:to_i)

    if n == 1
      if ts[0] != as[0]
        return 0
      else
        return 1
      end
    end

    if n == 2
      if ts[0] >= as[1]
        if as[0] != ts[0] || ts[1] != ts[0]
          return 0
        else
          return 1
        end
      else
        if as[0] != as[1] || ts[1] != as[0]
          return 0
        else
          return 1
        end
      end
      100
    end

    ans = 1

    if as[0] > as[1]
      if as[0] != ts[0]
        return 0
      end
    else
      if ts[0] > as[0]
        return 0
      end
    end

    if ts[n-1] > ts[n-2]
      if ts[n-1] != as[n-1]
        return 0
      end
    else
      if ts[n-1] < as[n-1]
        return 0
      end
    end
    
    (1...n-1).each do |i|
      if ts[i] > ts[i-1]
        if as[i] > as[i+1]
          if as[i] != ts[i]
            return 0
          end
        else
          if ts[i] > as[i]
            return 0
          end
        end
      else
        if as[i] > as[i+1]
          if ts[i] < as[i]
            return 0
          end
        else
          ans *= [as[i], ts[i]].min
          ans %= 1000000007
        end
      end
    end
    ans
  end
end

if $0 == __FILE__
  puts Alipnists.new.solve
end