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())
ball = list(map(int, input().split()))
ball.sort(reverse = True)
ok = {}
for x in ball:
    if x in ok:
        ok[x] += 1
    else:
        ok[x] = 1
ans = 0
for x in ball:
    if ok[x] != 0:
        y = 2**(x.bit_length()) - x
        if y in ok:
            if ok[y] != 0:
                if y == x and ok[y] == 1: 
                    continue
                ans += 1
                ok[x] -= 1
                ok[y] -= 1
print(ans)

