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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <iterator>
#include <cstdint>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define dump(x)  cerr << #x << " = " << (x) << endl;
using namespace std;
int combination(int n, int r) {
  if ( r * 2 > n ) r = n - r;
  int dividend = 1;
  int divisor  = 1;
  for ( int i = 1; i <= r; ++i ) {
    dividend *= (n-i+1);
    divisor  *= i;
  }
  //dump(r);
  //dump ( dividend / divisor);
  return dividend / divisor;
}
int main(){
  int n;
  cin >> n;
  int a[n];
  FOR(i,0,n){
    cin >> a[i];
  }
  sort(a,a + n);
  cout << a[n -1] << " ";
  int half = a[n -1] / 2;
  int ind = 0;
  FOR(i,0,n-1){
    if(a[i] > half){
      ind = i;
      break;
    }
  }
  int ans = 1;
  if(ind != 0) ans = combination(a[n-1],a[ind]);
  //dump(ans);
  int ansind = ind;
  FOR(i,1,2){
    int index = ind + i;
    if(a[index] == 0){
      if(ans <= 1) ansind = index;
    }else if(index < n-1 && ans <= combination(a[n-1],a[index])){
      ansind = index;
    }
    index = ind -i;
    if(a[index] == 0){
      if(ans <= 1) ansind = index;
    }else if(index >= 0 && ans <= combination(a[n-1],a[index]) ){
      ansind = index;
    }
  }
  //dump(a[ansind]);
  cout << a[ansind] << endl;
  return 0;
}