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
import collections
n = int(input())
a = list(map(int, input().split()))

memo = collections.defaultdict(lambda : 0)

for i in a:
    memo[i] = memo[i] + 1

b = sorted(memo.keys(), reverse=True)

ret = 0
pot = [1] * 35
for i in range(len(pot)-1):
    pot[i+1] = pot[i] * 2

for i in b:
    for j in range(34, -1, -1):
        if pot[j] - i <= 0:
            t = pot[j+1] - i
            break

    if i == t:
        ret += memo[i] // 2
    else:
        c = min([memo[i], memo[t]])
        memo[t] -= c
        ret += c

print(ret)