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 {
  def main(args: Array[String]): Unit = {
    var n = io.StdIn.readLine().toInt
    val t = io.StdIn.readLine().split(' ').map(_.toLong)
    val a = io.StdIn.readLine().split(' ').map(_.toLong)

    val h = scala.collection.mutable.ListBuffer.empty[Long]

    if (t(0) > a(0)) {
      println(0)
      return
    } else {
      if (n > 1 && a(0) > a(1) && t(0) != a(0)) {
        println(0)
        return
      } else {
        h += t(0)
      }
    }

    for (i <- 1 to (n - 2)) {
      val ht = if (t(i - 1) < t(i)) t(i) else 0
      val ha = if (a(i) > a(i + 1)) a(i) else 0
      if (ht == 0) {
        h += ha
      } else if (ha == 0) {
        h += ht
      } else if (ht == ha) {
        h += ha
      } else {
        println(0)
        return
      }
    }

    if (t(n - 1) < a(n - 1)) {
      println(0)
      return
    } else {
      if (n > 1 && t(n - 2) < t(n - 1) && t(n - 1) != a(n - 1)) {
        println(0)
        return
      } else {
        h += a(n - 1)
      }
    }

    val candidate = scala.collection.mutable.ListBuffer.empty[(Long, Int)]
    var j = 0
    while (j < n) {
      if (h(j) > 0) {
        j += 1
      } else {
        var k = j
        while (h(k) == 0) {
          k += 1
        }
        candidate += Tuple2(Math.min(h(j - 1), h(k)), k - j)
        j = k
      }
    }

    val p = Math.pow(10, 9).toLong + 7

    val res = candidate.foldLeft(1L) { (acc, pair) =>
      (acc * Math.pow(pair._1 % p, pair._2).toLong % p) % p
    }

    println(res)
  }

}