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
N=int(input())
A=sorted([int(i) for i in input().split()],reverse=True)
B=[2**(len(bin(i))-2) for i in A]
D=dict()
for i in range(N):
    if not(A[i] in D):
        D[A[i]]=1
    else:
        D[A[i]]+=1
ans=0
for i in range(N):
    if D[A[i]]<=0:
        continue
    if B[i]==2*A[i]:
        if D[A[i]]>=2:
            D[A[i]]-=2
            ans+=1
    else:
        if (B[i]-A[i]) in D:
            if D[B[i]-A[i]]!=0:
                D[A[i]]-=1
                D[B[i]-A[i]]-=1
                ans+=1
print(ans)
