Greatest Common Divisor (GCD) is a fundamental concept in mathematics that helps us understand the relationship between two numbers. It is the largest positive integer that divides two different numbers without leaving a remainder.

Finding GCD is an important skill that can be used in many areas of mathematics, including algebra, number theory, and cryptography. For example, in cryptography, the security of some encryption schemes depends on the complexity of finding the GCD of two large prime numbers.

One day, Alex decided to challenge himself by inventing his own encryption algorithm using GCD. He studied various encryption methods and was inspired to create something new and unique.

Instead of using large prime numbers, he decided to encode his data with a single array of positive integers $$$a_1, \ldots, a_n$$$. This array only has meaning if it is ordered in a certain way, so Alex properly shuffled his array.

Alex knew that the original order had a very special property: the numbers $$$(a_i + i)$$$ were not coprime. More formally, the condition $$$\text{GCD}(a_1 + 1, a_2 + 2, \ldots, a_n + n) \neq 1$$$ was satisfied.

Soon Alex realized that deciphering his cipher was far from an easy task. He already has a shuffled array $$$a_1, \ldots, a_n$$$ of length $$$n$$$. Help him restore the original order of the array or tell Alex that such an order does not exist and he made a mistake somewhere. If there can be multiple orders, any of them can be output.