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: Runtime Error)

from math import log2
from bisect import bisect_left


def getComp(n):
    return (1 << (1 + int(log2(n)))) - n


N = int(input())
A = [int(s) for s in input().split()]
A.sort()
avail = [True for _ in range(len(A))]

count = 0
for i in range(len(A) - 1, -1, -1):
    if not avail[i]:
        continue
    comp = getComp(A[i])
    j = bisect_left(A, comp)
    while True:
        if A[j] != comp:
            break
        if i == j or not avail[j]:
            j += 1
            continue
        avail[i] = False
        avail[j] = False
        count += 1
        break

print(count)