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
d = defaultdict(int)
n = int(input())
l = sorted(list(map(int,input().split())))
for i in l:
    d[i] += 1

ans = 0
for i in range(n-1,-1,-1):
    if d[l[i]] == 0:
        continue
    x = 2**(l[i].bit_length())
    y = x-l[i]
    if y == l[i]:
        if d[y] >= 2:
            d[y] -= 2
            ans += 1
    else:
        if d[y] > 0:
            d[y] -= 1
            d[l[i]] -= 1
            ans += 1
            
print(ans)