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()
A.reverse()
c = Counter(A)
ans = 0
# 大きいものからペアを探す
# 選択する数をx,ペアをyとする(1 <= y <= x)
# x < x+y <= 2*x よりxに対してx+yが2のべき乗となるようなものは一意に定まる
# したがってyも一意に定まるので,あとはyを探してくる
# x,yのペアが見つかれば1カウント
for e in A:
# x == y のとき １ループで2個減っているのでチェックする前にc[e] == 0となる可能性あり
    if c[e] == 0:
        continue
    c[e] -= 1
    pair = pow(2,e.bit_length()) - e
    if c[pair] >= 1:
        ans += 1
        c[pair] -= 1
print(ans)