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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func main() {
	sc.Split(bufio.ScanWords)

	n := nextInt()

	cm := make(map[int]int)
	as := make([]int, n)
	for i := 0; i < n; i++ {
		as[i] = nextInt()
		cm[as[i]]++
	}
	sort.Ints(as)

	ans := 0
	for i := 0; i < n; i++ {
		a := as[n-i-1]
		if cm[a] == 0 {
			continue
		}

		a2 := 1
		for a2 <= a {
			a2 *= 2
		}
		b := a2 - a

		if (b != a && cm[b] >= 1) || (b == a && cm[b] >= 2) {
			cm[a]--
			cm[b]--
			ans++
		}
	}
	fmt.Println(ans)
}

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}