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
size_a = int(input())
a = Counter(int(x) for x in input().split())
keys = list(a.keys())
keys.sort()
pair_cnt = 0
while size_a >= 2:
    x = keys[-1]
    if a[x] == 0:
        keys.pop()
        continue
    a[x] -= 1
    size_a -= 1
    if a[x] == 0:
        keys.pop()
    b = 2 ** x.bit_length() - x
    if a[b] > 0:
        a[b] -= 1
        size_a -= 1
        if a[b] == 0:
            del a[b]
        pair_cnt += 1
print(pair_cnt)