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: Time Limit Exceeded)

N = int(input())
aA = sorted([int(_) for _ in input().split()],reverse=True)
#aA1 = [ _ for _ in aA if _ % 2 ]
#aA0 = [ _ for _ in aA if _ % 2 == 0 ]


def searchPair(aD):
    iL = len(aD)
    dsT =set()
    iC = 0
    for i in range(iL):
        for j in range(i+1,iL):
            if i in dsT or j in dsT:
                continue
            iWa =  aD[i] + aD[j]
            if not ( iWa & (iWa - 1)):
                dsT.add(i)
                dsT.add(j)
                iC += 1

    return iC
iC = 0
#iC += searchPair(aA1)
#iC += searchPair(aA0)
iC += searchPair(aA)
print(iC)