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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

"use strict";

function getPair(num) {
  return (
    parseInt(
      num
        .toString(2)
        .split("")
        .map(x => (x === "1" ? "0" : "1"))
        .reduce((acc, cur) => acc + cur, ""),
      2
    ) + 1
  );
}

function main(input) {
  const inputs = input.split("\n").filter(x => x !== "");

  const A = inputs[1].split(" ").map(Number);

  let sortedA = A.sort((a, b) => b - a);
  let count = 0;
  while (sortedA.length > 0) {
    let i = sortedA[0];
    sortedA.splice(0, 1);

    let j = getPair(i);

    let indexJ = sortedA.findIndex(x => x === j);

    if (indexJ >= 0) {
      sortedA.splice(indexJ, 1);
      count++;
    }
  }

  console.log(count);
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));