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
import bisect

N = int(input())
A = list(map(int, input().split()))
L2 = [1]
for i in range(40):
    L2.append(L2[-1]*2)
D = defaultdict(int)
for a in A:
    D[a] += 1
A.sort(reverse=True)
res = 0
for a in A:
    if D[a] < 1:
        continue
    D[a] -= 1
    beki2 = L2[bisect.bisect_right(L2, a)]
    j = beki2 - a
    if D[j] > 0:
        D[j] -= 1
        res += 1

print(res)
