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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let t: Vec<usize> = (0..n).map(|_| it.next().unwrap().parse().unwrap()).collect();
    let a: Vec<usize> = (0..n).map(|_| it.next().unwrap().parse().unwrap()).collect();
    let mut l = vec![(1, 1_000_000_000); n];
    l[0] = (t[0], t[0]);
    for i in 1..n {
        if t[i - 1] < t[i] {
            l[i] = (t[i], t[i]);
        } else {
            l[i] = (1, t[i]);
        }
    }
    let mut r = vec![(1, 1_000_000_000); n];
    r[n - 1] = (a[n - 1], a[n - 1]);
    for i in (0..(n - 1)).rev() {
        if a[i] > a[i + 1] {
            r[i] = (a[i], a[i]);
        } else {
            r[i] = (1, a[i]);
        }
    }
    const MOD: usize = 1_000_000_007;
    let mut ans = 1;
    for i in 0..n {
        let x = std::cmp::max(l[i].0, r[i].0);
        let y = std::cmp::min(l[i].1, r[i].1);
        if x > y {
            ans = 0;
        } else {
            ans = ans * (y - x + 1) % MOD;
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}