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: Accepted)

from bisect import bisect_left, bisect_right
from collections import deque

N = int(input())
A = list(map(int, input().split(" ")))
A.sort()
A = deque(A)
ans = 0
t_max = len(bin(A[-1])) - 2
for t in range(t_max, 0, -1):
    if len(A) < 2: break
    while len(bin(A[-1])) - 2 > t:
        A.pop()
        if len(A) < 2: break
    if len(A) < 2: break
    pow2 = 1 << t
    A_tmp = deque()
    while t == len(bin(A[-1])) - 2:
        r = A.pop()
        idx = bisect_left(A, pow2 - r)
        for _ in range(idx):
            A_tmp.appendleft(A.popleft())
        if len(A) == 0: break
        if A[0] + r == pow2:
            A.popleft()
            ans += 1
        if len(A) < 2: break
    A.extendleft(A_tmp)
                    
print(ans)