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: Wrong Answer)

import bisect
N=int(input())
alist=list(map(int,input().split()))
alist.sort()

cand_list=[]
for i in range(1,N):
  a=a2=alist[i]
  digit_a2=0
  while(a2>0):
    a2>>=1
    digit_a2+=1  
  b=2**(digit_a2)-a
  #print(a,b)
  
  x=bisect.bisect_left(alist,b,hi=i-1)
  if alist[x]==b:
    #print(a,alist[x])
    cand_list.append((a,alist[x]))

cand_list.sort(reverse=True)
#print(cand_list)

answer_set=set()
used_set=set()
for i,j in cand_list:
  if (not i in used_set) and (not j in used_set):
    answer_set.add((i,j))
    used_set.add(i)
    used_set.add(j)
    
#print(answer_set)
print(len(answer_set))