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: Wrong Answer)

#![allow(unused_imports)]
#![allow(unused_macros)]
#![allow(unknown_lints)]
#![allow(unused_variables)]
#![allow(unused_must_use)]
#![allow(unused_mut)]
#![allow(dead_code)]
#![allow(unused_assignments)]

use std::collections::HashMap;
use std::process::exit;
use std::io::{
    stdin,
    stdout,
    stderr,
    Read,
    Write,
    BufReader,
    BufWriter
};

macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), stderr());
            writeln!(err, "\x1B[33m{}\x1B[0m = {:?}", e, $e).unwrap()
        })*
    };
}

macro_rules! stdin {
    () => ({
        use std::io::Read;
        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    })
}

macro_rules! test {
    ($($input:expr => $output:expr),* $(,)*) => (
        #[test]
        fn solve_test() {
            $(
                assert_eq!(solve($input.to_string()), $output);
            )*
        }
    )
}

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    println!("{}", solve(stdin!()));
}

fn solve(src: String) -> String {
    let mut res = String::from("");
    input!{
        source = src,
        n: usize,
        a: [i32; n]
    }
    let mut gcds: Vec<i32> = Vec::new();
    let mut check: Vec<i32> = Vec::new();
    check.push(0);
    for i in 0..n {
        for x in 1..a[i]+1 {
            if check.len() <= x as usize {
                for _ in check.len()..x as usize + 1 {
                    check.push(0);
                }
            }
            if a[i] % x == 0 {
                check[x as usize] += 1;
            }
        }
    }
    debug!(check);
    let mut max = 0;
    for i in 0..check.len() {
        if check[i] == n as i32 - 1 {
            max = i;
        }
    }
    debug!(max);
    res.push_str(&max.to_string());
    res.push_str("\n");
    res
}