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 = [int(i) for i in input().split()]

c = Counter(A)
b = sorted(c.keys())

ret = 0
for j in range(len(c) - 1, -1, -1) :
    i = 2
    while c[b[j]] > 0 and i - b[j] <= b[j] :
        if b[j] != i - b[j] :
            if c[b[j]] > 0 and c[i-b[j]] > 0 :
                M = min(c[b[j]], c[i-b[j]])
                ret += M
                c[b[j]] -= M
                c[i-b[j]] -= M
        else :
            if c[b[j]] > 1 :
                ret += c[b[j]] // 2
                c[b[j]] %= 2
        i *= 2
    
print(ret)
