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
from collections import Counter

read = sys.stdin.read
readline = sys.stdin.readline

N, *A = map(int, read().split())

A.sort()
a = Counter(A)
answer = 0
# 可能な最大の2冪
limit = 1 << ((2 * 10 ** 9 + 1).bit_length() - 1)

while A:
    n = A.pop()
    if a[n] == 0:
        continue

    a[n] -= 1
    s = limit
    while n < s:
        b = s - n
        if a[b] > 0:
            answer += 1
            a[b] -= 1
            break
        s //= 2

print(answer)
