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 collections
def hoge(n):
    k = 1    
    while k<=n:
        k*=2
    return k-n
ans = 0
input()
a = [int(x) for x in input().split()]
c = collections.Counter(a)
sa = list(set(a))
sa.sort()
sa.reverse()
for i in range(len(sa)):
    x = sa[i]
    if c[x]<= 0:
        continue    
    y = hoge(x)
    if x==y:
        ans += c[x]//2
    elif c[y]>= 0:
        ans += min(c[x],c[y])
        c[y] -=c[x]
print(ans)