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
#最大要素の相手は一意?

from collections import Counter
n = int(input())
a = list(map(int, input().split( )))
a_c = Counter(a)

a.sort(reverse = True)
ans = 0
for i in range(n):
    if not a_c[a[i]]:
        continue
    a_c[a[i]] -= 1
    t = (1<<a[i].bit_length()) - a[i]
    if t in a_c:#1つしか残っていないときに誤ってペアができていた
        if a_c[t]:
            a_c[t] -= 1
            #a_c[a[i]] -= 1#こっちも減らす
            ans += 1

print(ans)
            