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: Runtime Error)

import numpy as np
import bisect

N = int(input())
A = sorted(list(map(int, input().split())))

A = np.array(A)
AA = np.array(A)

beki = [2]
while beki[-1]*2 <= A[-1]+A[-2]:
    beki.append(beki[-1]*2)

beki = beki[::-1]
ans = 0
ind = 0
for b in beki:
    for i in range(N):

        if len(AA) <= 1:
            break

        tar = b - AA[ind]

        ind1 = bisect.bisect_left(AA,AA[ind],0,len(AA))
        ind2 = bisect.bisect_left(AA,tar,ind1,len(AA))

        if AA[ind2] == tar:
            AA = np.delete(AA,ind1)
            AA = np.delete(AA,ind2-1)
            ans += 1

        else:
            ind += 1

        if len(AA) <= 1:
            break

print(ans)