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: Runtime Error)

#include <stdio.h>

#define N 200000
#define A 100000

int main(void) {
    unsigned long int i, j, n, pair = 0;
    unsigned long int a[A+1];
    unsigned long int sum, t;

    scanf("%lu", &n);

    for (i=0; i<n; i++) {
        scanf("%lu", &a[i]);
    }

    for (i=0; i<n; i++) {
        for (j=i+1; j<n; j++) {
            sum = a[i] + a[j];
            for (t=1; t < sum; t = t*2) {;}
            if (sum%t == 0) {pair++;}
        }
    }
    printf("%lu\n", pair);
    return 0;
}