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 bisect  import bisect_left

n = int(input())
a = list(map(int,input().split()))
a.sort()
#print(a)

sum = 0
for i in range (len(a)-1,-1,-1):

    b = 1
    while b <= a[i]:
        b = b<<1
    t = b - a[i]
    #print("2^",t)

    k = bisect_left(a,t)
    if a[k] == t and k < i:
        sum += 1
        a[k] -= 0.1
        a[i] += 0.1
print(sum)