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 collections import Counter
from math import log2

def find(x):
    f = 2**(int(log2(x))+1)-x
    if f <= x:
        return f
    return 0

n = int(input())
a = list(map(int,input().split()))
a.sort(reverse = True)
c = Counter(a)
ans = 0

for i in range(n):
    f = find(a[i])
    if f == a[i]:
        m = c[a[i]]//2
    else:
        m = min(c[a[i]],c[f])
    c[a[i]] -= m
    c[f] -= m
    ans += m
print(ans)