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())
nums = sorted(list(map(int, input().split())), reverse=True)

num_map = Counter(nums)

answer = 0
for num in nums:
    pair = (1 << (num.bit_length())) - num

    if num_map[num] > 0 and num_map[pair]:
        if num == pair and num_map[num] > 1:
            answer += 1
            num_map[num] -= 2
        if not num == pair:
            answer += 1
            num_map[num] -= 1
            num_map[pair] -= 1

print(answer)