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 Kotlin (1.0.0) (judge verdict: Accepted)

val MOD = 1000000007L

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val t = readLine()!!.split(' ').map(String::toInt)
    val a = readLine()!!.split(' ').map(String::toInt)
    val amx = IntArray(n)
    val ans = IntArray(n)
    for (i in t.indices) {
        if (i != 0 && t[i - 1] > t[i]) {
            println(0)
            return
        }
        if (i == 0 || t[i - 1] < t[i]) {
            ans[i] = t[i]
        } else {
            amx[i] = t[i]
        }
    }
    for (i in t.indices.reversed()) {
        if (i != n - 1 && a[i + 1] > a[i]) {
            println(0)
            return
        }
        if (i == n - 1 || a[i + 1] < a[i]) {
            if (ans[i] != 0 && ans[i] != a[i] || amx[i] != 0 && amx[i] < a[i]) {
                println(0)
                return
            }
            ans[i] = a[i]
        } else {
            if (ans[i] != 0 && ans[i] > a[i]) {
                println(0)
                return
            }
            amx[i] = Math.min(amx[i], a[i])
        }
    }
    var res = 1L
    for (i in t.indices) {
        if (ans[i] == 0) res = (res * amx[i]) % MOD
    }
    println(res)
}