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 defaultdict

N=int(input())
A=[int(x) for x in input().split()]
A.sort(reverse=True)

cnt=defaultdict(int)
for a in A:
  cnt[a]+=1

P2=[]
for i in range(1,32):
  P2.append(2**(32-i))

ans=0

for a in A:
  for b in P2:
    if a >= b or cnt[a] < 1:
      break
    else:
      if (cnt[b-a] > 0 and (b-a) != a) or (cnt[b-a] > 1 and (b-a) == a):
        ans+=1
        cnt[b-a]-=1
        cnt[a]-=1
        break

print(ans)