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
import bisect
N = int(input())
*A, = map(int,input().split())
B = {}
for a in A:B[a] = B.get(a,0) + 1
B = sorted(map(list,B.items()))
bl = bisect.bisect_left

ans = 0
while B:
    b,n = B.pop()
    c = (1<<(len(bin(b))-2)) - b
    if c==b :
        ans += n//2
        continue
    i = bl(B,[c,0])
    if i>=len(B): continue
    if B[i][0] == c:
        m = min(n,B[i][1])
        ans += m
        B[i][1] -= m
print(ans)