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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
#include <string>
#include <cstring>
#include <utility>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#define debug(x) cerr << #x << ':' << x << endl
#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
using namespace std;
typedef long long ll;


int gcd(int a, int b) {
    if(a<b) int tmp=a, a=b, b=tmp;
    if(b==0) return a;
    return gcd(b, a%b);
}


int main(){
    int n;
    cin >> n;
    int A[n];
    REP(i, n) cin >> A[i];

    int l_gcd[n+1], r_gcd[n+1];
    for(int i=0; i<=n; i++){
        if(i==0) l_gcd[i]=0;
        else l_gcd[i] = gcd(l_gcd[i-1], A[i-1]);
    }
    for(int i=n; 0<=i; i--){
        if(i==n) r_gcd[i]=0;
        else r_gcd[i] = gcd(r_gcd[i+1], A[i]);
    }

    int ma=-1;
    for(int i=0; i<=n-1; i++)
        ma = max(ma,gcd(l_gcd[i], r_gcd[i+1]));
    cout << ma << endl;
    return 0;
}