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 collections import defaultdict
import heapq

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

data=defaultdict(int)
for i in range(0,N):
    data[A[i]]+=1

A=[-A[i] for i in range(0,N)]
heapq.heapify(A)
count=0
while A:
    x=-heapq.heappop(A)
    if data[x]!=0:
        data[x]-=1
        y=2**(len(bin(x))-2)-x
        if data[y]!=0:
            data[y]-=1
            count+=1

print(count)