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)

const MOD: i64 = 1000000007;

fn main() {
  let n: usize = read();
  let mut vect: Vec<i64> = read_vec();
  let mut veca: Vec<i64> = read_vec();
  
  if vect[n-1] != veca[0] {
    println!("0");
    return;
  }
  
  vect.insert(0,0);
  veca.push(0);
  let udt = vect.windows(2).map(|w| if w[0]==w[1] {(w[1],false)} else {(w[1],true)});
  let uda = veca.windows(2).map(|w| if w[0]==w[1] {(w[0],false)} else {(w[0],true)});
  let udt2 = vect.windows(2).map(|w| if w[0]==w[1] {(w[1],false)} else {(w[1],true)});
  let uda2 = veca.windows(2).map(|w| if w[0]==w[1] {(w[0],false)} else {(w[0],true)});

  let invalid = |(hp1,hp2)| {
    match (hp1, hp2) {
      ((h1, true), (h2, true)) => h1 != h2,
      ((h1, true), (h2, false)) => h1 > h2,
      ((h1, false), (h2, true)) => h1 < h2,
      _ => false
    }
  };

  if udt2.zip(uda2).any(invalid) {
    println!("0");
    return;
  }

  let ans =
    udt.
    zip(uda).
    filter_map(|((h1,p1),(h2,p2))| if p1 || p2 {None} else {Some(std::cmp::min(h1,h2))}).
    fold(1, |a,x| (a*x) % MOD);
  
  println!("{}", ans);
}

fn read<T: std::str::FromStr>() -> T {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().parse::<T>().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
}