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 sys
import collections

def solve():
    N = int(sys.stdin.readline().rstrip())
    A = list(map(int,sys.stdin.readline().rstrip().split()))
    A = sorted(A, reverse=True)
    maxA = A[0]
    cntA = collections.Counter(A)

    ans = 0
    for a in A:
        if cntA[a] == 0:
            continue
        cntA[a] -= 1
        #print('a =',a)
        b = (1 << a.bit_length()) - a
        if cntA[b] > 0:
            cntA[b] -= 1
            ans += 1
    return ans

print(solve())

#  1  1  7   9
#     3  5   11
#        13
#     15
#  2  6  10
#     14
#  4  4  12
#
#  8
