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 <bits/stdc++.h>
 
#define rep(i, x, n) for (int i = x; i < n; i++)
typedef long long ll;
 
const int INF = 1e9 + 7;
 
using namespace std;
 
ll gcd(ll n, ll k)
{
    if (k == 0)
	return n;
    ll mod = n % k;
    return gcd(k, mod);
}
 
int main()
{
    cin.tie(0); ios::sync_with_stdio(false);
    int n;
    cin >> n;
 
    vector<int> a(n);
    rep (i, 0, n)
	cin >> a[i];
 
    int l_gcd[n + 1];
    int r_gcd[n + 1];
    l_gcd[0] = 0;
    r_gcd[n] = 0;
 
    rep (i, 1, n) {
	l_gcd[i] = gcd(l_gcd[i - 1], a[i - 1]);
	r_gcd[n - i] = gcd(r_gcd[n - i + 1], a[n - i]);
    }
 
    int res = 0;
    rep (i, 0, n)
	res = max(res, (int)gcd(l_gcd[i], r_gcd[i + 1]));
 
    cout << res << endl;
 
    return 0;
}