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;
use std::cmp;

fn main() {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    let n: usize = s.trim().parse().unwrap();

    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    let xs: Vec<u64> = s.trim().split(' ').map(|x| x.parse().unwrap()).collect();

    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    let ys: Vec<u64> = s.trim().split(' ').map(|x| x.parse().unwrap()).collect();

    let mut tbs = vec![false; n];

    let mut p = 0;
    for i in 0..n {
        if p < xs[i] {
            tbs[i] = true;
            p = xs[i];
        }
    }

    let mut abs = vec![false; n];

    p = 0;
    for j in 1..(n + 1) {
        let i = n - j;

        if p < ys[i] {
            abs[i] = true;
            p = ys[i];
        }
    }

    let m = 1000000007;

    let mut r = 1;
    for i in 0..n {
        if tbs[i] && abs[i] && xs[i] != ys[i]{
            r = 0;
            break;
        }
        else if !tbs[i] && !abs[i] {
            r *= cmp::min(xs[i], ys[i]);
            r %= m;
        }
        else if tbs[i] != abs[i] {
            if (tbs[i] && xs[i] > ys[i]) || (abs[i] && ys[i] > xs[i]) {
                r = 0;
                break;
            }
        }
    }

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