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

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

def nibeki(x):
    cnt = 0
    while(x>1):
        x //=2
        cnt += 1
    return 2**(cnt+1)

cntSet = 0
c = Counter(a)
ks = list(c.keys())
ks.sort(reverse=True)

for k in ks:
    pair = nibeki(k)-k
    if k==pair:
        cntSet += c[k]//2

    elif c[k]>0 and c[pair]>0:
        COUNT = min(c[k], c[pair])
        c[k] -= COUNT
        c[pair] -= COUNT
        cntSet +=COUNT

print(cntSet)