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)

# coding: utf-8
# Your code here!

import bisect

N = int(input())
X = sorted(list(map(int, input().rstrip().split(' '))), reverse=False)
pow_2 = [2**i for i in range(40)]

count = 0
is_used = [False] * N
for i, x in enumerate(X[::-1]): 
    if is_used[i] == False:
        index1 = bisect.bisect_left(pow_2, x)
        index2 = bisect.bisect_left(X, pow_2[index1] - x)
        if pow_2[index1] - x == X[index2]:
            is_used[-i-1] = True
            is_used[index2] = True
            count += 1
        
print(count)