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 (1.42.0) (judge verdict: Accepted)

use itertools::Itertools;
use num::integer::gcd;
use proconio::input;
use proconio::marker::{Chars, Usize1};
use std::cmp::*;
use std::collections::*;
use std::iter::Iterator;

#[allow(unused_macros)]
macro_rules! max {
    ($x:expr) => {
      $x
    };
    ($x:expr, $($xs:tt)+) => {
      max($x,max!($($xs)+))
    };
  }

#[allow(unused_macros)]
macro_rules! min {
    ($x:expr) => {
      $x
    };
    ($x:expr, $($xs:tt)+) => {
      min($x,min!($($xs)+))
    };
  }

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

fn main() {
    input! {
    n: usize,
    mut a: [u64; n],
    }

    let mut l_gcd = vec![0; n+2];
    l_gcd[1] = a[0];
    for i in 1..n {
        l_gcd[i+1] = gcd(a[i], l_gcd[i]);
    }
 
    let mut r_gcd = vec![0; n+2];
    r_gcd[n] = a[n-1];
    for i in (0..n-1).rev() {
        r_gcd[i+1] = gcd(a[i], r_gcd[i+2]);
    }
    
    let mut ans = 1;
    for i in 0..n {
        let res = gcd(l_gcd[i], r_gcd[i+2]);
        ans = max(ans, res);
    }
    println!("{}", ans);

}