Problem:
Score : 600 points

Problem Statement

Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i.
He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Note that a ball cannot belong to multiple pairs.
Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

1 \leq N \leq 2\times 10^5

1 \leq A_i \leq 10^9

A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val n = readLine()!!.toLong()
    val aList = readLine()!!.split(' ').map(String::toLong).sorted().toMutableList()

    val bekiList = mutableListOf<Long>()
    var temp = 2L
    while (temp < 2000000000) {
        bekiList.add(temp)
        temp *= 2
    }
    bekiList.reverse()

    var pair = 0L
    while (true) {
        if (aList.size <= 1) break
        val p1 = aList.last()
        aList.removeAt(aList.size - 1)
        for (beki in bekiList) {
            val first = aList.fastIndexOfFirst { it == beki - p1 }
            if (first != -1) {
                pair++
                aList.removeAt(first)
                break
            }
        }
    }
    print(pair)
}


inline fun <T> List<T>.fastIndexOfFirst(predicate: (T) -> Boolean): Int {
    var left = 0
    var right = size - 1
    if(predicate(this[left])){
        return left
    }
    var allFalse = true
    while (left < right) {
        val index = ((left + right) / 2)
        if (predicate(this[index])) {
            right = index
            allFalse = false
        } else {
            left = index + 1
        }
    }
    return when {
        predicate(this[left]) -> left
        allFalse -> return -1
        else -> left - 1
    }
}