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 math
from collections import defaultdict
N = int(input())
A = sorted(int(i) for i in input().split())

d = defaultdict(lambda: 0)
for i in A:
    d[i] += 1

c = 0
for k in sorted(d.keys(), reverse=True):
    l = 2**int(math.log(k, 2) + 1) - k
    v = d[k]
    if k == l:
        c += v // 2
    elif l in d:
        w = d[l]
        if v > w:
            c += w
            d[l] = 0
        else:
            c += v
            d[l] = w-v
print(c)
