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)

use std::cmp::max;
use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let a: Vec<u64> = (0..n).map(|_| read()).collect();

    let gcd_n = a.iter().fold(a[0], |a, x| gcd(a, *x));

    if n == 2 {
        let ans = max(a[0], a[1]);
        println!("{}", ans);
        return;
    }

    let mut j = 0;
    for (i, a_i) in a.iter().enumerate() {
        if is_prime(a_i / gcd_n) {
            j = i;
            break;
        }
    }

    let mut ans = if j != 0 { a[0] } else { a[1] };

    for i in 0..n {
        if i != j {
            ans = gcd(ans, a[i]);
        }
    }
    println!("{}", ans);
}

fn is_prime(n: u64) -> bool {
    for i in 2..n.isqrt() + 1 {
        if n % i == 0 {
            return false;
        }
    }
    true
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|b| b.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn gcd(n: u64, m: u64) -> u64 {
    if n % m == 0 {
        m
    } else {
        gcd(m, n % m)
    }
}

trait IntegerSqrt {
    fn isqrt(&self) -> Self;
}

impl IntegerSqrt for u64 {
    fn isqrt(&self) -> Self {
        if *self < 2 {
            *self
        } else {
            let s = (*self >> 2).isqrt() << 1;
            let l = s + 1;
            if l * l > *self {
                s
            } else {
                l
            }
        }
    }
}