Problem:
Score : 400 points

Problem Statement

Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order.
From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized.
If there are multiple pairs that maximize the value, any of them is accepted.

Constraints

2 \leq n \leq 10^5

0 \leq a_i \leq 10^9

a_1,a_2,...,a_n are pairwise distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print a_i and a_j that you selected, with a space in between.

Sample Input 1

5
6 9 4 2 11

Sample Output 1

11 6

\rm{comb}(a_i,a_j) for each possible selection is as follows:

\rm{comb}(4,2)=6

\rm{comb}(6,2)=15

\rm{comb}(6,4)=15

\rm{comb}(9,2)=36

\rm{comb}(9,4)=126

\rm{comb}(9,6)=84

\rm{comb}(11,2)=55

\rm{comb}(11,4)=330

\rm{comb}(11,6)=462

\rm{comb}(11,9)=55

Thus, we should print 11 and 6.

Sample Input 2

2
100 0

Sample Output 2

100 0

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
#define ALL(x) (x).begin(),(x).end()
#define COUT(x) cout<<(x)<<"\n"
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define REP(i, n) for(int i=0;i<n;i++)
#define YES(x) cout<<(x?"YES":"NO")<<"\n"
#define Yes(x) cout<<(x?"Yes":"No")<<"\n"
#define dump(x) cout<<#x<<" = "<<(x)<<"\n"
#define endl "\n"
using G = vector<vector<int>>;
using M = map<int,int>;
using P = pair<int,int>;
using PQ = priority_queue<int>;
using PQG = priority_queue<int,vector<int>,greater<int>>;
using V = vector<int>;
using ll = long long;
using edge = struct { int to; int cost; };
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
const int INF = 1e9;
const int MOD = 1e9+7;
const ll LINF = 1e18;

ll choose(ll n, ll a) {
  ll x = 1, y = 1;
  REP(i,a) {
    x *= n-i;
    y *= i+1;
  }
  return x / y;
}

int main() {
  IOS;
  ll n; cin >> n;
  vector<ll> a(n); REP(i,n) cin >> a[i];
  sort(ALL(a));

  ll ma = a[a.size()-1];
  ll last = -1;
  REP(i,n-1) {
    ll cur = choose(ma,a[i]);
    if (cur <= last) {
      cout << ma << " " << a[i-1] << endl;
      return 0;
    }
    last = cur;
  }
  cout << ma << " " << a[n-2] << endl;
  return 0;
}