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, = map(int, input().split())
cnt = Counter(A)
A = sorted(A, reverse=True)
ans = 0
for a in A:
    if a & (a - 1) != 0:
        cand = (1 << ((a - 1).bit_length())) - a
        if cnt[a] == 0 or cnt[cand] == 0: continue
    else:
        cand = a
        if cnt[a] < 2: continue
    ans += 1
    cnt[a] -= 1; cnt[cand] -= 1
print(ans)