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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <stdint.h>
#include <string.h>

uint32_t numList[100000];

int cmpfunc(const void * a, const void * b) {
	return *(uint32_t *)b - *(uint32_t *)a;
}

static uint32_t getCombDiff(const uint32_t i, const uint32_t j) {
	return j < i / 2 ? j : i - j;
}

static uint64_t calcComb(const uint64_t i, const uint64_t j) {
	uint64_t product = UINT64_C(1);

	for (uint64_t ii = 0; ii < j; ii++) {
		product *= i - ii;
	}
	for (uint64_t ii = 1; ii <= j; ii++) {
		product /= ii;
	}

	return product;
}

static void printMaxComb(const uint32_t * const numList, const uint32_t listSize) {
	uint32_t maxI = 0, maxJ = 1;
	uint64_t maxComb = 0;

	for (uint32_t i = 0; i < listSize - 1; i++) {
		uint32_t maxDiff = 0;
		for (uint32_t j = i + 1; j < listSize; j++) {
			const uint32_t diff = getCombDiff(numList[i], numList[j]);
			if (diff >= maxDiff) {
				maxDiff = diff;
			}
			else {
				const uint64_t comb = calcComb((uint64_t)(numList[i]), (uint64_t)(getCombDiff(numList[i], numList[j - 1])));
				if (comb > maxComb) {
					maxComb = comb;
					maxI = i;
					maxJ = (i == j - 1) ? j : j - 1;
				}
			}
		}
	}

	printf("%"PRIu32" %"PRIu32, numList[maxI], numList[maxJ]);
}

int main(void) {
	uint32_t listSize;

	scanf("%"PRIu32"\n", &listSize);

	for (uint32_t idx = 0; idx < listSize - 1; idx++) {
		scanf("%"PRIu32" ", &(numList[idx]));
	}
	scanf("%"PRIu32, &(numList[listSize - 1]));

	qsort(numList, listSize, sizeof(uint32_t), cmpfunc);

	printMaxComb(numList, listSize);

	return 0;
}