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)
cnt = Counter(a)
ans = 0

def make(x):
    num = 1
    while num <= x:
        num *= 2
    return num

for i in range(n):
    x = make(a[i])
    if cnt[x - a[i]] > 0 and cnt[a[i]] > 0 and x != 2 * a[i]:
        ans += 1
        cnt[x - a[i]] -= 1
        cnt[a[i]] -= 1
    elif x == 2 * a[i] and cnt[a[i]] > 1:
        ans += 1
        cnt[a[i]] -= 2

print(ans)