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 (2.4.0) (judge verdict: Time Limit Exceeded)

from collections import defaultdict
N = int(input())
a = list(map(int, input().split()))
pow2 = [2 ** i for i in range(61)]
a = sorted(a, reverse=True)
d = defaultdict(int)
for i in a:
    d[i] += 1


num = 0
for i in range(N):
    for k in range(60):
        if pow2[k] - a[i] != a[i]:
            if d[pow2[k] - a[i]] > 0 and d[a[i]] > 0:
                num += 1
                d[pow2[k] - a[i]] -= 1
                d[a[i]] -= 1
                break
        else:
            if d[a[i]] >= 2:
                num += 1
                d[a[i]] -= 2
                break
print(num)