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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main extends App {
  import scala.io.StdIn._

  val n = readInt
  val t = readLine.trim.split(' ').map(_.toInt)
  val a = readLine.trim.split(' ').map(_.toInt)
  var isParadoxical = false
  val confirmed = Array.tabulate(n){_ ⇒ -1}
  confirmed(0) = t.head
  confirmed(n - 1) = a.last
  for (i ← t.indices.tail){
    if (confirmed(i) != -1 && confirmed(i) != t(i)) isParadoxical = true
    if (t(i) != t(i - 1)){
      confirmed(i) = t(i)
    }
  }
  for (i ← a.indices.reverse.tail){
    if (confirmed(i) != -1 && confirmed(i) != a(i)) isParadoxical = true
    if (a(i) != a(i + 1)){
      confirmed(i) = a(i)
    }
  }
  val mod = 1000000007L
  if (isParadoxical) println(0)
  else {
    var count = 1L
    val mountains = confirmed.indices.filter(i ⇒ confirmed(i) != -1).toArray
    for (i ← mountains.indices.tail){
      count *= expWithMod(math.min(confirmed(mountains(i)), confirmed(mountains(i - 1))), mountains(i) - mountains(i - 1) - 1)
      count %= mod
    }
    println(count)
  }
  def expWithMod(base: Long, exp: Int): Long = {
    exp match {
      case 0 ⇒ 1
      case 1 ⇒ base
      case _ ⇒ expWithMod(base, exp / 2).let(it ⇒ (it * it % mod) * expWithMod(base, exp % 2)) % mod
    }
  }

  implicit class Scope[T](val value: T) extends AnyVal {
    @inline def also(@inline func: T ⇒ Unit): T = {
      func(value)
      value
    }
    @inline def let[A](@inline func: T ⇒ A): A = func(value)
  }
}