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

# 入力
N = int(input())
A = list(map(int, input().split()))

# 最大の整数が書かれているボールから順に貪欲的にペアを作成する。
C = Counter(A)
ans = 0
for m in sorted(C, reverse=True):
    p = (1 << m.bit_length()) - m
    if m == p:
        ans += C[m] // 2
    elif p in C:
        k = min(C[m], C[p])
        ans += k
        C[p] -= k

# 出力
print(ans)
