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
from math import *
 
n=int(raw_input())
arr=list(map(int,raw_input().split()))
dict1={}
for i in range(n):
    val=arr[i]
    try:
        dict1[val]+=1
    except:
        KeyError
        dict1[val]=1
#print(dict1)
ans=0
arr.sort(reverse=True)
for i in range(n):
    if(dict1[arr[i]]>0):
        xd=2**(len(bin(arr[i]))-2)
        if(xd-arr[i]!=arr[i]):
            try:
                if(dict1[xd-arr[i]]>0):
                    ans+=1
                    dict1[xd-arr[i]]-=1
                    dict1[arr[i]]-=1
            except:
                KeyError
        else:
            if(dict1[arr[i]]>1):
                ans+=1
                dict1[arr[i]]-=2
print(ans)