p03201 AtCoder Grand Contest 029 - Powers of two
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
```python
from collections import Counter

N = int(input())
As = list(map(int, input().split()))

cnt = Counter(As)
As.sort(reverse=True)

Ps = [2]
for i in range(29):
    Ps.append(Ps[-1] * 2)

ans = 0
for A in As:
    if cnt[A] <= 0: continue
    cnt[A] -= 1

    while Ps[-1] > 2 * A:
        Ps.pop()

    if cnt[Ps[-1] - A] > 0:
        ans += 1
        cnt[Ps[-1] - A] -= 1

print(ans)

```