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 PYTHON):

Solution:
from collections import Counter, defaultdict, deque
import bisect
from sys import stdin, stdout
from itertools import repeat
import math
import timeit

def inp(force_list=False):
    re = map(int, raw_input().split())
    if len(re) == 1 and not force_list:
        return re[0]
    return re

def inst():
    return raw_input().strip()

def gcd(x, y):
   while(y):
       x, y = y, x % y
   return x

MOD = 998244353

def sq(a, b):
    re = 1
    while b:
        if b&1:
            re *= a
            re %= MOD
        a *= 8
        a %= MOD
        b >>= 1
    return re

def inv(num):
    return sq(num, MOD-2)

def my_main():
    kase = 1#inp()
    pans = []
    for _ in xrange(kase):
        n = inp()
        ans = []
        tt = 1
        for i in range(1, n):
            if gcd(i, n)==1:
                ans.append(i)
                tt*=i
                tt%=n
        if tt!=1:
            ans.remove(tt)
        pans.append(str(len(ans)))
        pans.append(' '.join(map(str, ans)))
    print '\n'.join(map(str, pans))

my_main()