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 Counter
if __name__ == "__main__":
    N=int(input())
    lista=list(map(int,input().split()))
    mii=Counter(lista)
    si=set(lista)
    listb=[i for i in si]
    listb.sort()
    ans=0
    while(len(listb)>0):
        x=listb.pop()
        if mii[x]>0:
            k=1
            while k<=x:
                k*=2
            y=k-x
            if x==y:
                ans+=mii[x]//2
            elif y<x and y in si:
                m=min(mii[x],mii[y])
                ans+=m
                mii[y]-=m
            mii[x]=0
    print(ans)