Product of numbers

Given a set of $n$ natural numbers, choose any subset $S$ such that $\prod_{x \in S} \equiv 1 \pmod{n}$ .

Input

Input consists of several cases. Every case begins with $n$ , followed by $n$ different numbers, all between 1 and $10^9$ . Assume $2 \le n \le 10^5$ .

It is easy to see that no number $x$ where $\mbox{gcd}(x, n) \ne 1$ could ever be part of any solution. Consequently, every given $x$ is such that $\mbox{gcd}(x, n) = 1$ .

Output

Print one line for every case, with a non-empty subset of the given numbers such that the product of its elements is congruent with 1 modulo $n$ . Each number can be used at most once. Print the numbers in any order, and separated by one space. If there are several solutions, print any of them. If there is no solution, print “Maths are difficult”.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:15:56.363Z