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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<(n);i++)
typedef long long ll;
typedef pair<int,int> P;
ll gcd(ll a, ll b) {
    if(a%b == 0) return b;
    else return gcd(b,a%b);
}
int main(void) {
    int n; cin >> n;
    vector<ll> a(n);
    rep(i, n) cin >> a[i];
    int cand1 = a[0], cand2 = a[1];
    for(int i=2;i<n;i++) {
        cand1 = gcd(cand1, a[i]);
        cand2 = gcd(cand2, a[i]);
    }
    cout << max(cand1, cand2);
}