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

N = int(input())
a = sorted(list(map(int,input().split())))

count = 0

b = {}
for i in range(len(a)):
    if a[i] in b:
        b[a[i]] += 1
    else:
        b[a[i]] = 1

for i in range(len(a) - 1, -1, -1):
    if  b[a[i]] == 0:
        continue
    temp = a[i]
    b[a[i]] -= 1
    s=2**math.floor(math.log2(temp))
    st = 2*s - temp 
    if a ==[]:
        break
    if st in b and b[st] > 0:
        b[2*s-temp] -= 1
        count += 1
    
print(count)

