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_arr = list(map(int, input().split()))

A_arr = sorted(A_arr, reverse=True)
C_arr = Counter(A_arr)

count = 0
for i in range(N):
    v_max = A_arr[i]
    if C_arr[v_max] == 0:
        continue
    C_arr[v_max] -= 1
    v_pair = 2**v_max.bit_length() - v_max
    if C_arr[v_pair] > 0:
        C_arr[v_pair] -= 1
        count += 1
    else:
        pass

print(count)