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: Wrong Answer)

# coding: utf-8
# Your code here!

import bisect

n=int(input())
a = [int(i) for i in input().split()]
a.sort()
check = [0]*n
print(a)

ans=0

while(a):
    c=a.pop()
    d=c
    keta=0
    while(d!=0):
        d=d//2
        keta +=1
    x = 2**keta - c
#    print(c,x)
    i = bisect.bisect_left(a, x)
    if i != len(a) and a[i] == x:
        ans += 1
#        print(a[i],c,"xxx")
        a.remove(x)



print(ans)