Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer $$$n$$$. Initially the value of $$$n$$$ equals to $$$v$$$ and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer $$$x$$$ that $$$x<n$$$ and $$$x$$$ is not a divisor of $$$n$$$, then subtract $$$x$$$ from $$$n$$$. The goal of the player is to minimize the value of $$$n$$$ in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
The input contains only one integer in the first line: $$$v$$$ ($$$1 \le v \le 10^9$$$), the initial value of $$$n$$$.
Output a single integer, the minimum value of $$$n$$$ the player can get.
In the first example, the player can choose $$$x=3$$$ in the first turn, then $$$n$$$ becomes $$$5$$$. He can then choose $$$x=4$$$ in the second turn to get $$$n=1$$$ as the result. There are other ways to get this minimum. However, for example, he cannot choose $$$x=2$$$ in the first turn because $$$2$$$ is a divisor of $$$8$$$.
In the second example, since $$$n=1$$$ initially, the player can do nothing.
Origin Avito Cool Challenge 2018
AC Rate 68.42%
Date 03/04/2019 16:43:11