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 bisect
import itertools
from collections import defaultdict
N = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
d = defaultdict(int)

for key, value in itertools.groupby(a):
    d[key] = len(list(value))

ans = 0
for i in range(N):
    now = a[i]
    if d[now] > 0:
        pair = 2**((now).bit_length()) - now
        if now == pair:
            if d[pair] >= 2:
                ans += 1
                d[pair] -= 2
        elif d[pair] > 0:
            ans += 1
            d[now] -= 1
            d[pair] -= 1
print(ans)
