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
# -*- coding: utf-8 -*-
import collections

N = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
c=collections.Counter(A)

pairCounter=0

beki=29
nibeki=2**beki

for i in range(N):
  target = A[i]
  if c[target] < 1:
    continue
  c[target]-= 1

  while (nibeki > target):
    beki-=1
    nibeki=2**beki

  pair = nibeki * 2 - target
  if pair in c.keys() and c[pair] > 0:
    c[pair]-= 1
    pairCounter+=1

print(pairCounter)