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)

N=int(input())
A=list(map(int,input().split()))

from collections import Counter
counter=Counter(A)

LIST=sorted(list(counter.keys()),reverse=True)

L=len(LIST)

i=0
ANS=0
while i<L:
    #print(i,counter,ANS)
    if counter[LIST[i]]==0:
        i+=1
    else:
        for k in range(33):
            if 2**k<=LIST[i]:
                continue
            if 2**k>LIST[i]*2:
                i+=1
                break
            if counter.get(2**k-LIST[i],0)>0:
                if LIST[i]!=2**k-LIST[i]:                        
                    counter[LIST[i]]-=1
                    counter[2**k-LIST[i]]-=1
                    ANS+=1
                else:
                    if counter[LIST[i]]>=2:
                        counter[list[i]]-=2
                        ANS+=1
                    

print(ANS)