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
N = int(input())
a = list(map(int, input().split()))
a = sorted(a, reverse=True)

cnt = {}
for n in a:
    cnt[n] = cnt.get(n, 0) + 1

ans = 0
for n in a:
    g = 2 ** n.bit_length()
    s = g - n
    if n == s:
        pair = cnt.get(s, 0) // 2
        ans += pair
        cnt[s] = cnt.get(s, 0) % 2
    else:
        pair = min(cnt.get(n, 0), cnt.get(s, 0))
        ans += pair
        cnt[n] = cnt.get(n, 0) - pair
        cnt[s] = cnt.get(s, 0) - pair
print(ans)
