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 CPP):

Solution:
#include<bits/stdc++.h>
#define top 1000000007
#define max(a,b) (a>b) ? a:b
#define min(a, b) (a<b) ? a:b
#define S second
#define F first
using namespace std;
const long long p = 1e8 +1;
long long get_min(long long a, long long b, long long c, long long d) { long long x= min(a,b); x =min(x,d); return min(x,c);}

int gcd(int a, int b)
{
    if(b == 0) return a;
    return gcd(b, a%b);
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    // cout<<gcd(12, 55);
    vector <int> v{};
    int n;
    cin>>n;
    long long pro =  1;
    v.emplace_back(1);
    for(int i=2; i<n; ++i)
    {
        if(gcd(i, n) == 1){
            pro*=i; 
            pro%=n;
            v.emplace_back(i);
        } 
    }
    if(pro!=1){
        auto it = find(v.begin(), v.end(), pro);
        if(it!=v.end()) v.erase(it);
    }
    cout<<v.size()<<endl;
    for(int i=0; i<v.size();++i)
        cout<<v[i]<<" ";
	return 0;
}