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 = list(map(int, input().split()))
a.sort(reverse=True)
d = dict()
ans = 0
for x in a:
  if x not in d:
    d[x] = 0
  d[x] += 1
for x in a:
  t = (1<<x.bit_length()) - x
  f = (d.get(t,0) and d.get(x,0))
  if t == x:
    f = (d.get(t,0) >= 2)
  if f:
    d[x] -= 1
    d[t] -= 1
    ans += 1
print(ans)