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.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
import bisect

def binum(num):
	number_len = len(bin(num))-2
	f = 2**number_len -1
	return (num^f)+1

N = int(input())
A = list(map(int, input().split()))
A.sort()
cnt = 0

while len(A) > 0:
	k = A.pop()
	if len(A) == 0:
		break
	if int(k) != k:
		continue
	x = binum(k)
	if x > A[-1]:
		continue
	if A[bisect.bisect_left(A,x)] == x:
		A[bisect.bisect_left(A,x)] -= 0.5
		cnt += 1

print(cnt)
