The chosen one

#include <bits/stdc++.h>

using namespace std;

typedef unsigned long long ll;
const ll MAX=1e5+5;
ll age[MAX];
ll pore[MAX];
int main()
{
    int n;
    cin >> n;
    ll a[n];
    ll m=0;
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
        m=max(m,a[i]);
    }
    for(int i=1;i<n;i++)
    {
        age[i]=__gcd(age[i-1],a[i-1]);
    }
    for(int i=n-2;i>=0;i--)
    {
        pore[i]=__gcd(pore[i+1],a[i+1]);
    }
    for(int i=0;i<n;i++)
    {
        ll ans=__gcd(age[i],pore[i]);
        if( ans!= 0 && a[i]%ans!=0)
        {
            cout<<ans<<endl;
            return 0;
        }
    }
    cout<<m+1<<endl;
}