Problem:
Score : 300 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case)]

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

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        a
    } else {
        gcd(b, a%b)
    }
}

fn main() {
    let N: usize = read_line().parse().unwrap();
    let A = read_vec();

    let mut left = vec![0; N];
    let mut right = vec![0; N];

    left[0] = A[0];
    for i in 1..N {
        left[i] = gcd(left[i-1], A[i]);
    }
    right[N-1] = A[N-1];
    for i in (0..N-1).rev() {
        right[i] = gcd(right[i+1], A[i]);
    }

    let mut max = right[1];
    for i in 1..N-1 {
        max = std::cmp::max(max, gcd(left[i-1], right[i+1]));
    }
    max = std::cmp::max(max, left[N-2]);
    println!("{}", max);
}