Problem: Now you get Baby Ehab's first words: "Given an integer n, find the longest subsequence of [1,2, …, n-1] whose product is 1 modulo n." Please solve the problem.

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly all) elements. The product of an empty subsequence is equal to 1.

Input

The only line contains the integer n (2 ≤ n ≤ 10^5).

Output

The first line should contain a single integer, the length of the longest subsequence.

The second line should contain the elements of the subsequence, in increasing order.

If there are multiple solutions, you can print any.

Examples

Input


5


Output


3
1 2 3 

Input


8


Output


4
1 3 5 7 

Note

In the first example, the product of the elements is 6 which is congruent to 1 modulo 5. The only longer subsequence is [1,2,3,4]. Its product is 24 which is congruent to 4 modulo 5. Hence, the answer is [1,2,3].

Solution (in PYTHON3):

Solution:
from collections import *
from itertools import *
from random import  *
from bisect import *
from string import *
from queue import *
from heapq import *
from math import *
from sys import *
from re import *
def fast(): return stdin.readline().strip()
def zzz(): return [int(i) for i in fast().split()]


z, zz = input, lambda: list(map(int, z().split()))
szz, graph, mod, szzz = lambda: sorted(
    zz()), {}, 10**9 + 7, lambda: sorted(zzz())


def lcd(xnum1, xnum2): return (xnum1 * xnum2 // gcd(xnum1, xnum2))
def output(answer): stdout.write(str(answer))


dx = [-1, 1, 0, 0, 1, -1, 1, -1]
dy = [0, 0, 1, -1, 1, -1, -1, 1]


###########################---Test-Case---#################################
"""
  If you Know me , Then you probably don't know me !

"""
###########################---START-CODING---##############################

n = int(z())

prime = [1]*(n+10)

def SieveOfEratosthenes(n):
    prime = [True for i in range(n+1)]
    p = 2
    while(p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1
    return prime
prime=SieveOfEratosthenes(n+10)


def coprime(a, b):
    if gcd(a,b)==1:
        return True
    else:
        return False

res=0
lst=[]
p=1
for i in range(1,n):
    if coprime(i,n) :
        res+=1
        p*=i
        p%=n
        lst.append(i)


if p!=1:
    lst.remove(p)
print(len(lst))
print(*lst)