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
from collections import deque
import copy
import math
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline


def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N] = [int(input_raw[0])]
    A = []
    input_raw = read_func().strip().split()
    for i in range(N):
        A.append(int(input_raw[i]))

    pair_count = 0
    already_set = set([])
    for t in range(31, 0, -1):
        x = 2**t
        count_dict = {}
        for i in range(N):
            if i in already_set:
                continue
            if x - A[i] <= 0:
                continue
            if x - A[i] in count_dict and len(count_dict[x - A[i]]) > 0:
                pair_count += 1
                j = count_dict[x - A[i]].pop()
                already_set.add(i)
                already_set.add(j)
            else:
                if A[i] not in count_dict:
                    count_dict[A[i]] = [i]
                else:
                    count_dict[A[i]].append(i)

    print pair_count

if __name__ == '__main__':
    main()
