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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <string>
template <typename T>
inline bool Maximize(T& Target, T Value);
template <typename T>
inline bool Minimize(T& Target, T Value);

using namespace std;
using lli = long long;
const int maxN = 1e5;

int n;

int GCD(int x, int y)
{
    while (y != 0)
    {
        int r = x % y;
        x = y;
        y = r;
    }
    return x;
}

void Solve()
{
    int a = 1;
    for (int i = 1; i <= n - 2; ++i)
        if (GCD(n, i) == 1)
            a = (lli)a * i % n;
    int lim = (a == 1 && n > 2) ? n - 2 : n - 1;
    int res = 0;
    for (int i = 1; i <= lim; ++i)
        if (GCD(n, i) == 1)
            ++res;
    cout << res << '\n';
    for (int i = 1; i <= lim; ++i)
        if (GCD(n, i) == 1)
            cout << i << ' ';
}

int main()
{
    #ifndef cfc
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    #else
    freopen("input.txt", "r", stdin);
    #endif
    while (cin >> n)
        Solve();
}

template <typename T>
inline bool Maximize(T& Target, T Value)
{
    if (Value > Target)
    {
        Target = Value;
        return true;
    }
    return false;
}

template <typename T>
inline bool Minimize(T& Target, T Value)
{
    if (Value < Target)
    {
        Target = Value;
        return true;
    }
    return false;
}