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
import sys
input = sys.stdin.readline

from collections import Counter

# 最大値は相手が決まる -> greedy

N = int(input())
A = [int(x) for x in input().split()]

counter = Counter(A)
A.sort()

answer = 0
for x in A[::-1]:
    while counter[x] > 0:
        counter[x] -= 1
        target = (1 << x.bit_length()) - x
        if counter[target] > 0:
            counter[target] -= 1
            answer += 1

print(answer)

