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
n  =  int(input())
a  =  list(map(int, input().split()))
a.sort(reverse = True)
d  =  {}
count = 0

for x in a:
    if x not in d: d[x] = 0
    d[x] += 1
    
for i in range(len(a)):
    if d[a[i]] == 0:
        continue
        
    d[a[i]] -= 1
    
    y = 2**a[i].bit_length() - a[i]
    
    if y in d and d[y] > 0:
        count += 1
        d[y]  -= 1
        
print(count)