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 collections
n=int(input())
a=sorted(map(int,input().split()))[::-1]
s=collections.Counter(a)
r=0
flag=False
for i in range(n):
    #print(i,a[i])
    if flag:
        flag=False
        continue
    if s[a[i]]==0: continue
    pair = 2**math.ceil(math.log2(a[i]))-a[i]
    #print("pair",pair)
    if pair in s.keys() and s[pair]>0:
        s[a[i]]-=1
        s[pair]-=1
        r+=1
        continue
    if i<n-1 and pair==0 and a[i+1]==a[i] and s[a[i]]>=2:
        s[a[i]]-=2
        r+=1
        flag=True
print(r)