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:
def main():
    n = lie()
    if n <= 2:
        print('\n'.join(['1', '1']))
    elif n == 3:
        print(2)
        print(' '.join(['1', '3']))
    else:
        print(n)
        for i in range(2, n + 1, 2):
            print(i, end=' ')
        for i in range(1, n + 1, 2):
            print(i, end=' ')


def fun(m, n, s, k):
    return


def fun2(s):
    return


from sys import *
import inspect
import re
from math import *
import threading
from collections import *
from pprint import pprint as pp
mod = 998244353
MAX = 10**5


def lie():
    return int(input())


def liee():
    return map(int, input().split())


def array():
    return list(map(int, input().split()))


def deb(p):
    for line in inspect.getframeinfo(inspect.currentframe().f_back)[3]:
        m = re.search(r'\bdeb\s*\(\s*([A-Za-z_][A-Za-z0-9_]*)\s*\)', line)
        print('%s %d' % (m.group(1), p))


def vector(size, val=0):
    vec = [val for i in range(size)]
    return vec


def matrix(rowNum, colNum, val=0):
    mat = []
    for i in range(rowNum):
        collumn = [val for j in range(colNum)]
        mat.append(collumn)
    return mat


def dmain():
    setrecursionlimit(100000000)
    threading.stack_size(40960000)
    thread = threading.Thread(target=main)
    thread.start()


if __name__ == '__main__':
    # main()
    dmain()