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 = list(map(int, input().split()))
ans = 0

D = defaultdict(int)
for x in A:
    D[x] += 1
A.sort(reverse=True)

for x in A:
    for i in range(1, 31):
        if D[x] > 0:
            if 2**i-x in D.keys() and D[2**i-x] > 0:
                if 2**(i-1) != x:
                    ans += 1
                    D[x] -= 1
                    D[2**i-x] -= 1
for i in range(31):
    ans += D[2**i]//2
print(ans)