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())
xs = [int(w) for w in input().split()]

counter = Counter(xs)

descent = sorted(xs, reverse=True)

def minimal_greater_power(x):
    b = len("{0:b}".format(x))
    return 2 ** b

ans = 0

for x in descent:
    if x not in counter:
        continue
    if counter[x] == 0:
        continue

    counter[x] -= 1

    pair = minimal_greater_power(x) - x
    if pair not in counter:
        continue
    if counter[pair] == 0:
        continue

    ans += 1
    counter[pair] -= 1

print(ans)
