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 Counter

n = int(input())
A = list(map(int, input().split()))

A.sort(reverse=True)
c = Counter(A)

ans = 0
flag = False
for i in range(n):
    if c[A[i]] == 0:
        continue

    pow_2 = 2 ** len(format(A[i], "b"))
    if c[pow_2 - A[i]] > 0 and pow_2 - A[i] != A[i]:
        c[pow_2 - A[i]] -= 1
        c[A[i]] -= 1
        ans += 1
    elif c[pow_2 - A[i]] > 1 and pow_2 - A[i] == A[i]:
        if flag is True:
            c[A[i]] -= 2
            ans += 1
            flag = False
        else:
            flag = True

print(ans)