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)
C = Counter(A)
m = 1 << 30
ans = 0

for a in A:
    if C[a] <= 0:
        continue
    C[a] -= 1
    while m > a * 2:
        m >>= 1
    v = m - a
    if v in C and C[v] > 0:
        C[v] -= 1
        ans += 1

print(ans)