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

from collections import defaultdict
d = defaultdict(int)

for num in a:
    d[num]+=1

ans=0
for num in sorted(d,reverse=True):
    while d[num]>=1:
        d[num]-=1

        now=1
        while now<=num:
            now*=2

        cand = now - num
        if d[cand]>=1:
            d[cand]-=1
            ans+=1
        else:
            break
print(ans)