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 Python (3.4.3) (judge verdict: Wrong Answer)

def main():
    n = int(input())
    nums = list(map(int, input().split()))
    nums.sort()
    used = [False] * n

    num_bin_digits = [1 << len("{:b}".format(x)) for x in nums]
    cnt = 0

    for cur in reversed(range(n)):
        if used[cur]:
            continue

        num = nums[cur]
        power_of_2 = num_bin_digits[cur]
        pair = power_of_2 - num
        idx = -1
        if pair in nums[:cur]:
            idx = nums.index(pair)

        if idx != -1 and not used[idx]:
            used[idx] = True
            cnt += 1

        #print(idx, num, power_of_2, pair)
        #print(used)

    print(cnt)

    return

main()