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 bisect
N=int(input())
A=list(map(int,input().split()))
A.sort()
A.append(999999999999999)
B=[]
for i in range(1,35):
    B.append(2**i)
ans=0
for i in range(N):
    if A[N-1-i]==int(A[N-1-i]):
        for j in range(len(B)):
            if A[N-1-i]<B[j]:
                break
        if A[bisect.bisect_left(A,B[j]-A[N-1-i])]==B[j]-A[N-1-i]:
            if bisect.bisect_left(A,B[j]-A[N-1-i])<N-1-i:
                A[bisect.bisect_left(A,B[j]-A[N-1-i])]-=0.1
                A[N-1-i]+=0.1
                ans+=1
print(ans)