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: Accepted)

from bisect import bisect_left
N=int(input())
A=list(map(int,input().split()))
B=[0]*N
A.sort()
t=0
for i in range(N):
    while 2**t<=A[i]:
        if 2**t<=A[i]<2**(t+1):
            break
        t+=1
    B[i]=2**(t+1)-A[i]
i=N-1
count=0
flag=[0]*N
for i in range(N-1,0,-1):
    if flag[i]==1:
        continue
    flag[i]=1
    b=bisect_left(A,B[i])
    if A[b]==B[i] and flag[b]==0:
        flag[i]=1
        flag[b]=1
        A[b]-=1
        count+=1
print(count)