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
def twopower(n):
    for i in range(32):
        if n < 2**i:
            return 2**i
N = int( input())
A = list( map( int, input().split()))
d = defaultdict( int)
e = defaultdict( int)
for i in range(N):
    d[A[i]] += 1
A.sort(reverse=True)
i = 0
ans = 0
while i < N:
    if e[A[i]] >= d[A[i]]:
        i += 1
        continue
    e[A[i]] += 1
    L = twopower(A[i]) - A[i]
    if e[L] < d[L]:
        ans += 1
        e[L] += 1
    i += 1
print(ans)
