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().strip())
data = list(reversed(sorted(map(int, input().split()))))

cnt = {x: 0 for x in data}
for x in data:
    cnt[x] += 1

ans = 0
t = 2 ** 30
for x in data:
    while t // 2 > x:
        t = t // 2
    while cnt[x] > 0:
        cnt[x] -= 1
        if t-x in cnt and cnt[t-x] > 0:
            cnt[t-x] -= 1
            ans += 1

print (ans)

