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 defaultdict

n = int(input())
a = list(map(int,input().split()))
a2 = list(set(a))
a2.sort(reverse=True)

d = defaultdict(int)
for i in a:
    d[i] += 1

ans = 0
for i in a2:
    next = 2**(i-1).bit_length()
    if(i==next):
        ans += d[i]//2
    else:
        pair = min(d[i],d[next-i])
        d[next-i] -= pair
        ans += pair
print(ans)