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: Wrong Answer)

from bisect import bisect_left
import sys

input = sys.stdin.buffer.readline

n = int(input())
A = list(map(int, input().split()))
A.sort()
used = [False] * (n)
ans = 0
for i in range(n - 1, -1, -1):
    used[i] = True
    num = A[i]
    temp = num // (num & -num)
    keta = temp.bit_length()
    kouho = 1
    for i in range(1, keta):
        if (temp >> i) & 1 == 0:
            kouho += 1 << i
    kouho *= num & -num
    pos = bisect_left(A, kouho)
    if used[pos]:
        continue
    if A[pos] == kouho:
        # print(num, A[pos])
        used[pos] = True
        ans += 1

print(ans)