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 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>

int sort(const void *a, const void *b){
    return *(int*)b-*(int*)a ;
}

long long combination(int a,int b){
    long long combinationans=1;
    if (b>a/2){
        b=a-b;
    }
    for (int i=0; i<b; i++){
        combinationans=combinationans*(a-i)/(i+1);   
    }
    return (combinationans);
}

int main(void){
    long long ans=LLONG_MIN,tmp;
    int n;
    scanf("%d",&n);
    int a[n],tmpj,ansi,ansj;
    for (int i=0; i<n; i++){
        scanf("%d",&a[i]);
    }
    qsort (a,n,sizeof(int),sort); 
    for (int i=0; i<n; i++){
        tmpj=i+1;
        for (int j=i+1; j<n; j++){
            if (abs((a[i]/2)-a[j])<abs((a[i]/2)-a[tmpj])){
                tmpj=j;
            }
        }
        tmp=combination(a[i],a[tmpj]);
        if(ans<tmp){
            ans=tmp;
            ansi=a[i];
            ansj=a[tmpj];
        }
    }
    printf("%d %d\n",ansi,ansj);
	return 0 ;
}