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:
"""
ID: happyn61
LANG: PYTHON3
PROB: loan
"""
from itertools import product
import itertools
#from collections import defaultdict
import sys
import heapq
import math
from collections import deque
MOD=10**9+7
#fin = open ('loan.in', 'r')
#fout = open ('loan.out', 'w')
#print(dic["4734"])
def find(parent,i):


    if parent[i] != i: 
        parent[i]=find(parent,parent[i]) 
    return parent[i] 

        # A utility function to do union of two subsets 
def union(parent,rank,xx,yy): 
    x=find(parent,xx)
    y=find(parent,yy)
    if rank[x]>rank[y]:
        parent[y]=x
    elif rank[y]>rank[x]:
        parent[x]=y
    else:
        parent[y]=x
        rank[x]+=1
def factorof(div,n):
	if (n%div) == 0:
		return True
	else:
		return False
		
def minfactor(n):
	for i in range(2,n+1):
		if(factorof(i,n)):
			return i
			
def factoring(n):
	fct=[]
	while n>1:
		f=minfactor(n)
		n=n//f
		match=False
		for i in range(0,len(fct)):
			if fct[i][0] == f:
				fct[i][1]=fct[i][1]+1
				match=True
				break
			if fct[i][0]>f:
				break
		if not match:
				fct.append([f,1])
	return fct	    
ans=0
#NK=sys.stdin.readline().strip().split()
K=int(sys.stdin.readline().strip())
#N=int(NK[0])
#K=int(NK[1])
#M=int(NK[2])
#ol=list(map(int,sys.stdin.readline().strip().split()))
#d={0:0,1:0}
from math import gcd as bltin_gcd
def coprime2(a, b):
    return bltin_gcd(a, b) == 1
x=0
y=0
#l=factoring(K)
ans=1
l=[]
for n in range(1,K):
    if coprime2(n,K):
        l.append(n)
        ans*=n
        ans=ans%K
if ans%K!=1:
    l.pop()
print(len(l))
for i in range(len(l)):
    l[i]=str(l[i])
print(" ".join(l))
#d={"N":(0,1),"S":(0,-1),"W":(-1,0),"E":(1,0)}