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 math
N = int(input())
A = list(map(int,input().split()))
D = {}
for i in A :
    if i in D :
        D[i] += 1
    else :
        D[i] = 1

ans = 0
A = sorted(A,reverse=True)
for i in A :
    r = 2**math.ceil(math.log2(i))
    if i == r :
        ans += (D[i] // 2)
        D[i] = 0
    else :
        b = r-i
        if D[i] > 0 and D.get(b,0) > 0 :
            D[i] -= 1
            D[b] -= 1
            ans += 1
print(ans)
