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 = [int(i) for i in input().split()]

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

ans = 0
for a in A:
    if not cnt[a]: continue

    # aより大きい最小の2のべき乗
    p = 2 ** a.bit_length()
    if cnt[p - a]:
        if a == p - a:
            if cnt[a] >= 2:
                ans += 1
                cnt[a] -= 2
        else:
            ans += 1
            cnt[p - a] -= 1
            cnt[a] -= 1

print(ans)