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 collections import defaultdict
import sys
input = sys.stdin.readline

def main():
    n = int(input())
    alst = list(map(int, input().split()))
    alst.sort(reverse = True)
    max_a = alst[0]
    dd = defaultdict(int)
    for a in alst:
        dd[a] += 1
    i = 1
    while i <= max_a:
        i *= 2
    ans = 0
    for a in alst:
        if dd[a] <= 0:
            continue
        while i > a * 2:
            i /= 2
        dd[a] -= 1
        num = i - a
        if dd[num]:
            ans += 1
            dd[num] -= 1
    print(ans)
    
main()