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)

import bisect
from collections import Counter

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

two_bekis = [2**i for i in range(31)]

ans = 0
cnt = Counter(A)
seta = set(A)
for i, a in enumerate(reversed(A)):
    b = two_bekis[bisect.bisect_right(two_bekis, a)] - a
    if b not in seta:
        continue

    if a == b and cnt[a] >= 2:
        ans += 1
        cnt[a] -= 2
    elif a != b and cnt[a] >= 1 and cnt[b] >= 1:
        ans += 1
        cnt[a] -= 1
        cnt[b] -= 1
print(ans)