1865: Buttons 扣子

Background

As you surely already know, Yekaterinburg has gotten its right to hold The Summer Olympic Games of the 2032. It is planned that it will be allowed to Russia as a country-organizer to emend a program of the games a bit. So, in order to improve the command result it has been decided to replace the competition in gymnastics by the competition in the new game "Buttons".
The rules of the game are very simple. There's a small heap of K buttons before two players. The players in turns take buttons from the heap, moreover, at a time one can take a number of buttons from 1 up to L. The one who takes the last button is the winner.
Yekaterinburg获得了2032年夏季奥运会的举办权。由于允许举办国对竞赛项目进行一些小的修改。现打算修改“Button”这个新项目的规则。规则很简单，在2个对手前有一堆扣子（k个），2人轮流取走扣子，同一时间，某人能取走1至L个扣子。取走最后一个扣子的为胜者。
The rules of the Olympic Games will be a bit harder then usual. The one, who is to make a first step according to a lot, has an opportunity to fix a number K with the following restriction to it: 3 <= K <= 100 000 000 (that is the exact number of buttons that has been prepared for the Olympic tournament). The player who is to make the second step fixes a number L that satisfies the following conditions 2 <= L < K.
作为奥运会项目，规则应该比通常玩的要难一点。先走者可以设定数K（就是总共有k个扣子），3 <= K <= 100 000 000.后走者可以设定数L，2 <= L < K

Problem

A very crucial task is given to your team: you are to write a program that should help the second player to make his choice. In other words, given a number K your program is to find a number L that guaranties a victory to the second player with a proper game of both sides.
现在要紧的问题是，请你写一个程序，帮助后走者做出抉择。换言之，当给出K后，你的程序能给出数L，使到后走者能获胜。
So, for instance, there are only three buttons in the heap, the choice L = 2 provides for the victory of the second player. Really, if the first player takes only one button at his turn, the second one wins, taking the two last buttons. On the contrary, if the first one takes two buttons, the second one wins, taking the last button.
例如， 如果只有3个扣子，后走者把L定为2，有必胜把握。事实上，如果先走者取了1个扣子，那么后走者可以取剩下的2个扣子，后走者胜。如果先走者取了2个扣子，那么后走者取1个，也是后走者胜。

The standard input consists of one line, which contains an only integer number K ?a number of buttons in the heap, that has fixed the first player at his turn.
输入只包含一个整数K，扣子的总数。

To the standard output you are to write the only number L ?the maximal number of buttons that can be taken at a time which provides for the victory of the second player. If there are several those numbers L, you should write the least. If there are no such numbers, you are to write 0 to the standard output.
输出L。每次最多能取走的扣子总数，要求保证后走者必胜。假如有多个答案，输出最小的。如果不存在保证能必胜的L，则输出0。

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