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 Python (3.4.3) (judge verdict: Accepted)

import math
import bisect
n=int(input())
a=list(map(int,input().split()))
a.sort()
x=a[0]
ctn=1
l=[]
l2=[]
for i in range(1,n):
  if x==a[i]:
    ctn+=1
  else:
    l.append([x,ctn])
    l2.append(x)
    x=a[i]
    ctn=1
l.append([x,ctn])
l2.append(x)

b=[]
for i in range(1,50):
  b.append(2**i)

ct=0
for i in range(len(l2)-1,-1,-1):
    x=math.floor(math.log2(l2[i]))
    x=b[x]-l2[i]
    y=bisect.bisect_left(l2,x)
    if l2[y]==x:
      if l2[y]!=l2[i]:
        m=min(l[i][1],l[y][1])
      else:
        m=l[i][1]//2
      l[i][1]-=m
      l[y][1]-=m
      ct+=m
print(ct)