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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
using ll = long long;

int gcd(int n, int m) {
    if (n < m) swap(n, m);
    while (m != 0) {
        int r = n % m;
        n = m;
        m = r;
    }
    return n;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;

    vector<int> a(n), b(n + 1), c(n + 1);
    int r = 0;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        r = gcd(r, a[i]);
        b[i + 1] = r;
    }

    r = 0;
    for (int i = n - 1; i >= 0; i--) {
        r = gcd(r, a[i]);
        c[i] = r;
    }

    r = 0;
    for (int i = 0; i < n; i++) {
        r = max(r, gcd(b[i], c[i + 1]));
    }

    //a[0]を書き換えるなら、a[1]~a[n-1]のgcdでOK
    //a[0]を書き換えないなら、

    cout << r << endl;

    return 0;
}