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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

#define IS_SQUARE(i) (((i) & ((i) - 1)) == 0)

int qsort_compare_int(const void *a, const void *b)
{
    // 降順ソート
    return *(int*) b - *(int*) a;
}

int main(int argc, char *argv[])
{
    int n, i, j;
    int a[200000];
    int x, y;
    int count;

    scanf("%d", &n);
    for (i = 0; i < n; i++) {
        scanf("%d", &a[i]);
    }
    qsort(a, n, sizeof(int), qsort_compare_int); // 降順ソート

    count = 0;
    for (i = 0; i < n; i++) {
        x = a[i];
        if (x == 0) {continue;}
        for (j = i + 1; j < n; j++) {
            y = a[j];
            if (y == 0) {continue;}
            if (IS_SQUARE(x + y)) {
                count++;
                a[j] = 0;
                break;
            }
        }
    }

    printf("%d\n", count);

    return 0;
}