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

inputs.sort(reverse=True)
counter_inputs = Counter(inputs)
powers_of_two = [2**i for i in range(1, 31)]
ans = 0

for item in inputs:
    if counter_inputs[item] > 0:
        counter_inputs[item] -= 1
    
        while powers_of_two[-1] > 2 * item:
            powers_of_two.pop(-1)
        
        pair = powers_of_two[-1] - item
        if counter_inputs[pair] > 0:
            ans += 1
            counter_inputs[pair] -= 1
    
print(ans)
