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<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define sc(x) scanf("%d",&x);

ll fac(ll n){
    if (n < 2) return 1;
    return n * fac(n - 1);
}
ll COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac(n) / fac(k) / fac(n - k);
}

int main(){
    int n; sc(n)
    vector<int> A(n);
    for (int i = 0; i < n; i++) sc(A[i])
    sort(A.begin(), A.end());
    
    P ans = P(A[1], A[0]);
    ll maxv = COM(A[1], A[0]), tmp2;
    for (int i = 2; i < n; i++){
        auto tmp = upper_bound(A.begin(), A.end(), A[i]/2);
        if (A[i]/2 - *tmp < A[i]/2 - *(tmp+1) && *(tmp+1) <= A[i]) tmp++;
        tmp2 = COM(A[i], *tmp);
        if (tmp2 > maxv){
            maxv = tmp2;
            ans = P(A[i], *tmp);
        }
    }
    cout << ans.first << " " << ans.second << endl;
    return 0;
}