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)

import bisect

n = int(input())
a = list(map(int,input().split()))

a.sort()

b = [0]*n
ans = 0

for i in range(n):
    if b[-i-1]==0:
        c = 2**(len(bin(a[-i-1]))-2)-a[-i-1]
        d = bisect.bisect_left(a,c)
        e = bisect.bisect_right(a,c)
        if a[d]==c:
            for j in range(d,e):
                if b[j]==0 and j!=n-i-1:
                    ans += 1
                    b[-i-1]=1
                    b[j]=1
                    break

print(ans)