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

def get_smallest_power_of_2_over_N(N):
    i=2
    while i<=N:
        i*=2
    return i

N = int(input())
A = list(map(int,input().split()))


A = sorted(A)

ans=0
D=Counter(A)

for i in reversed(range(N)):
    pair_val = get_smallest_power_of_2_over_N(A[i]) - A[i]
    if D[A[i]]<=0:
        continue
    elif pair_val==A[i] and D[pair_val]>=2 or pair_val!=A[i] and  D[pair_val]>=1:
        ans+=1
        D[pair_val]-=1
        D[A[i]]-=1

print(ans)
