Problem: An exam for n students will take place in a long and narrow room, so the students will sit in a line in some order. The teacher suspects that students with adjacent numbers (i and i + 1) always studied side by side and became friends and if they take an exam sitting next to each other, they will help each other for sure.

Your task is to choose the maximum number of students and make such an arrangement of students in the room that no two students with adjacent numbers sit side by side.

Input

A single line contains integer n (1 ≤ n ≤ 5000) — the number of students at an exam.

Output

In the first line print integer k — the maximum number of students who can be seated so that no two students with adjacent numbers sit next to each other.

In the second line print k distinct integers a1, a2, ..., ak (1 ≤ ai ≤ n), where ai is the number of the student on the i-th position. The students on adjacent positions mustn't have adjacent numbers. Formally, the following should be true: |ai - ai + 1| ≠ 1 for all i from 1 to k - 1.

If there are several possible answers, output any of them.

Examples

Input

6

Output

6
1 5 3 6 2 4

Input

3


Output

2
1 3

Solution (in PYTHON3):

Solution:
from sys import stdin, stdout, stderr, setrecursionlimit
import inspect, re

setrecursionlimit(100000)

def debug (*e):
    if not __debug__:
        print(*e, file=stderr)

def dd(*vals):
    frame = inspect.getframeinfo(inspect.stack()[1][0])
    vs = re.search("dd\((.+)\)", frame.code_context[0]).group(1).split(",")
    if vs:
        debug(",".join("{0} = {1}".format(vs[i], v) for i,v in enumerate(vals)))

def trace(f):
    def traced(*args, **kw):
        debug("calling {} with args {}, {}".format(f.__name__, args, kw))
        return f(*args, **kw)
    return traced
#@trace
#def f(x):

def read():
    return stdin.readline().rstrip()

def readarr(sep=None, maxsplit=-1):
    return read().split(sep, maxsplit)

def readint():
    return int(read())

def readintarr(sep=None, maxsplit=-1):
    return [int(a) for a in readarr(sep, maxsplit)]

#write(1, 2, 3, sep="-", end="!")
def write(*args, **kwargs):
    sep = kwargs.get('sep', ' ')
    end = kwargs.get('end', '\n')
    stdout.write(sep.join(str(a) for a in args) + end)

#writearr([1, 2, 3], sep="-", end="!")
def writearr(arr, sep=' ', end='\n'):
    stdout.write(sep.join(str(a) for a in arr) + end)

from itertools import chain

n = readint()
disp = set(range(2, n+1))
ans = [1]
A = []
avance = True
while disp:
    if avance:
        sigs = chain(range(ans[-1]+3, n+1), [ans[-1]+2])
    else:
        sigs = range(ans[-2]+1, n+1)
    for x in sigs:
        if x in disp and abs(x-ans[-1])!=1:
            disp.remove(x)
            ans.append(x)
            break
    else:
        break
    avance = not avance
if n > 1:
    A = [0, 2]
    disp = set(range(1, n+1))
    avance = True
    while disp:
        if avance:
            sigs = chain(range(A[-1]+3, n+1), [A[-1]+2])
        else:
            sigs = range(A[-3]+1, n+1)
        for x in sigs:
            if x in disp and abs(x-A[-1])!=1:
                disp.remove(x)
                A.append(x)
                break
        else:
            break
        avance = not avance
    A = A[1:]

if len(ans) < len(A):
    ans = A

if n > 4 and n%2==1 or n > 3 and n%2==0:
    A = list(range(1, n+1, 2)) + list(range(2, n+1, 2))

if len(ans) < len(A):
    ans = A

write(len(ans))
write(" ".join(str(i) for i in ans))