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 PyPy3 (7.3.0) (judge verdict: Accepted)

from collections import defaultdict

n = int(input())
A = list(int(x) for x in input().split())

count = defaultdict(int)
for a in A:
    count[a] += 1
A = sorted(set(A))

ans = 0
for a in reversed(A):
    t = a.bit_length()
    pair = 2**t - a
    if pair == a:
        ans += count[a] // 2
        count[a] -= count[a] // 2
    else:
        k = min(count[a], count[pair])
        ans += k
        count[a] -= k
        count[pair] -= k

print(ans)