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
# Your code here!

import bisect
import collections

n=int(input())
a = [int(i) for i in input().split()]
a.sort()
#print(a)

checked=collections.Counter(a)

ans=0

while(a):
    c=a.pop()
    if checked[c]==0:
        continue
    checked[c]-=1
    d=c
    keta=0
    while(d!=0):
        d=d//2
        keta +=1
    x = 2**keta - c
#    print(c,x)
    i = bisect.bisect_right(a, x)
    if i and a[i-1] == x and checked[x]>0:
        ans += 1
        checked[x]-=1
        
#    print(checked)
#        print(checked)
#        print(a[i],c,"xxx")




print(ans)

