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
def main():
	from math import log,ceil
	n=int(input())
	a=list(map(int,input().split()))
	num={}
	for x in a:
		if x in num:
			num[x]+=1
		else:
			num[x]=1
	ans=0
	cnt=ceil(log(max(a),2)+1e-9)+1

	for i in range(cnt,0,-1):
		b={}
		for x in num:
			if 2**i-x in b:
				b[2**i-x]+=1
			else:
				b[2**i-x]=1
		for x in num:
			if x in b and num[x]>0:
				if x*2==2**i:
					ans+=num[x]//2
					num[x]%=2
				else:
					small=min(num[x],num[2**i-x])
					ans+=small
					num[x]-=small
					num[2**i-x]-=small
	print(ans)
if __name__ == '__main__':
	main()