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()))
A.sort(reverse = True)
d = {}
for a in A:
    if a in d:
        d[a] += 1
    else:
        d[a] = 1

ans =0
for a in A:
    b = 2**(a.bit_length())-a
    if b in d:
        if d[b] >=1 and d[a] >= 1:
          if a == b and d[b] ==1:
            continue
          ans += 1 
          d[b]-= 1
          d[a]-= 1

print(ans)
            