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 math,collections
n=int(input())
a=sorted(map(int,input().split()))[::-1]
s=collections.Counter(a)
r=0
f=0
for i,v in enumerate(a):
	p=2**math.ceil(math.log2(v))-v
	if f:f=0
	elif s[v]==0:pass
	elif p in s.keys()and s[p]>0:s[v]-=1;s[p]-=1;r+=1
	elif i<n-1 and p==0 and v==a[i+1]and s[v]>1:s[v]-=2;r+=1;f=1
print(r)