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 bisect import bisect
N = int(input())
*A, = map(int, input().split())
B = {}
for a in A:
    B[a] = B.get(a, 0) + 1
R = sorted(B.items())
C = []; D = []
for k, v in sorted(B.items()):
    C.append(k)
    D.append(v)
M = len(C)
j = 0
ans = 0
for i in range(M-1, -1, -1):
    if D[i] == 0:
        continue
    a = C[i]
    b = 2**a.bit_length()
    j = bisect(C, b-a-1)
    if j < M and C[j] == b-a:
        if i == j:
            c = D[i]//2
        else:
            c = min(D[i], D[j])
        ans += c
        D[i] -= c; D[j] -= c
print(ans)