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 defaultdict

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

a.sort()
memo = defaultdict(int)
for i in range(n):
    memo[a[i]] += 1

count = 0
for i in reversed(range(n)):
    if memo[a[i]] == 0:
        continue
    if (memo[(1 << (len(bin(a[i])) - 2)) - a[i]] > 0 and (1 << (len(bin(a[i])) - 2)) - a[i] != a[i]) or memo[(1 << (len(bin(a[i])) - 2)) - a[i]] > 1:
        memo[a[i]] -= 1
        memo[(1 << (len(bin(a[i])) - 2)) - a[i]] -= 1
        count += 1

print(count)