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
# cook your dish here
from collections import Counter
 
n = int(input())
a = list(map(int, input().split()))
a.sort()
a = a[::-1]
c = Counter(a)

res = 0
for x in a:
    b = 1
    while b <= x:
        b = b*2
    p = b-x
    if p in c.keys():
        if p == x and c[x] >= 2:
            c[x] = c[x] - 2
            res += 1
        elif p != x and c[x] > 0 and c[p] > 0:
            c[x] -= 1
            c[p] -= 1
            res += 1
    
print(res)