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)

N = int(input())
A = list(map(int,input().split(" ")))
'''
N = 5
A = [3,11,14,5,13]
'''

def check(a,b):
	i = 2
	while(True):
		n = 2**i
		if a+b < n:
			return False
		if a+b == n:
			return True
		i+=1


def ans(A,n):
	if len(A) <= 1:
		return n
	a = A[0]
	bs = A[1:]
	m = []
	flag = False
	for p,b in enumerate(bs):
		if check(a,b):
			flag = True
			n+=1
			m.append(ans(bs[:p]+bs[p+1:],n))
	if not flag:
		return ans(A[1:],n)
	return max(m)


print(ans(A,0))