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)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn readln<T>() -> T
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().parse().unwrap()
}

#[derive(Clone, Copy, Eq, PartialEq, Debug)]
enum E {
    Answer(u64),
    Less(u64),
}

use std::cmp;

fn main() {
    let n = readln();
    let xs = reads();
    let ys = reads();

    let mut zs = vec![E::Less(1000000000); n];

    let mut prev = 0;
    for (i, x) in xs.into_iter().enumerate() {
        if x > prev {
            prev = x;
            zs[i] = E::Answer(x);
        }
        else {
            zs[i] = E::Less(x);
        }
    }

    let mut prev = 0;
    let mut flag = true;
    for i in 0..n {
        let i = n - i - 1;
        let y = ys[i];

        if !flag {
            break;
        }

        if y > prev {
            prev = y;

            match zs[i] {
                E::Answer(n) if n == y => {},
                E::Less(n) if n >= y => {zs[i] = E::Answer(y);},
                _ => {flag = false;},
            }
        }
        else {
            match zs[i] {
                E::Answer(n) if y >= n => {},
                E::Less(n) => {zs[i] = E::Less(cmp::min(n, y));},
                _ =>  {flag = false;},
            }
        }
    }

    let mut res = 0;
    if flag {
        res = 1;
        for z in zs {
            if let E::Less(n) = z {
                res *= n;
                res %= 1000000007;
            }
        }
    }

    println!("{}", res);
}