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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val n= readLine()!!.toInt()
    val a= readLine()!!.split(" ").map { it.toInt() }.sorted()

    val max = a.last()
    val half_r = a.lowerBound((1+max)/2)
    val half_l = half_r-1
    if(half_l==-1) {
        println("$max 0")
        return
    }
    val ans = if( Math.abs(max*0.5-a[half_l]) < Math.abs(max*0.5-a[half_r]) ) a[half_l] else a[half_r]
    println("$max $ans")

}

//ソート済みのListに対して、log(size)回の比較でelementより(真に)小さい要素の個数(element以上の要素が初めて現れるindex)を返す。
fun <T : Comparable<T>> List<T>.lowerBound(element: T, fromIndex: Int = 0, toIndex: Int = size): Int {
    var low = fromIndex
    var high = toIndex

    while (low < high) {
        val mid = (low + high).ushr(1)
        val cmp = get(mid).compareTo(element)

        if (cmp < 0)
            low = mid + 1
        else //(cmp >= 0)
            high = mid
    }
    return low
}