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 typing import List
from math import gcd

def optimal(size: int) -> List[int]:
    invalid, valid = 1, list()
    for value in range(1, size):
        if not gcd(size, value) - 1:
            valid.append(value)
            invalid = (invalid * value) % size
    invalid = None if not invalid - 1 else invalid
    return [item for item in valid if item != invalid]


def read_input(filename: str = None) -> None:
    from sys import stdin
    stdin = open(filename) if filename else stdin
    size = int(stdin.readline())
    valid = optimal(size)
    print(len(valid))
    print(*valid)


def main():
    read_input()


if __name__ == '__main__':
    main()