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
#設定
import sys
input = sys.stdin.buffer.readline

from collections import defaultdict

def getlist():
	return list(map(int, input().split()))


#処理内容
def main():
	#前処理
	N = int(input())
	A = getlist()
	D = defaultdict(int)
	for i in A:
		D[i] += 1
	L = []
	for i in D:
		L.append(i)
	L = sorted(L)
	#print(L)
	
	#貪欲
	ans = 0
	for i in range(len(L)):
		a = L[-1 - i]
		if a == 2 ** (a.bit_length() - 1):
			ans += int(D[a] // 2)
		else:
			b = 2 ** a.bit_length() - a
			m = min(D[a], D[b])
			ans += m
			D[a] -= m
			D[b] -= m

	#出力
	print(ans)

if __name__ == '__main__':
	main()