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())
A = list(map(int,input().split(" ")))
A.sort()
used = [0] * N
pow2_set = reversed([ 1<<i for i in range(36)])
ans = 0
for pow2 in pow2_set:
    l,r = 0,N-1
    while l < r:
        if A[l] + A[r] < pow2:
            l += 1
        elif A[l] + A[r] == pow2:
            if used[l] == 0 and used[r] == 0:
                ans += 1
                used[l],used[r] = 1,1
            else:
                if used[l] == 1:
                    l += 1
                if used[r] == 1:
                    r -= 1
        else:
            r -= 1
 
print(ans)