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
import bisect
n=int(input())
a=list(map(int,input().split()))
a.sort()

x=a[0];ctn=1;l=[];l2=[]
for i in range(1,n):
  if x==a[i]:
    ctn+=1
  else:
    l.append([x,ctn])
    l2.append(x)
    x=a[i]
    ctn=1
l.append([x,ctn])
l2.append(x)

b=[2**i for i in range(1,50)]

ct=0
for i in range(len(l2)-1,-1,-1):
  x=math.floor(math.log2(l2[i]))
  x=b[x]-l2[i]
  y=bisect.bisect_left(l2,x)
  if l2[y]==x:
    if l2[y]!=l2[i]:
      m=min(l[i][1],l[y][1])
    else:
      m=l[i][1]//2
    l[i][1]-=m
    l[y][1]-=m
    ct+=m
print(ct)