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
n=int(input())
a=sorted(list(map(int,input().split())),reverse=1)
b=Counter(a)
cnt=0
for i in range(n):
    if b[a[i]]<=0:
        continue
    k=a[i].bit_length()
    x=(1<<k)-a[i]
    if x==a[i]:
        if b[x]>1:
            cnt+=1
            b[x]-=2
    elif x in b and b[x]>0:
        cnt+=1
        b[a[i]]-=1
        b[x]-=1
print(cnt)