Ural 1023. Buttons

1023. Buttons

Time limit: 2.0 second

Memory limit: 64 MB

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.

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 ≤ 108 (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 conditions2 ≤ 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.

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.

Input

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.

Output

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.

Sample

input	output
3	2

Problem Author: Leonid Volkov

Problem Source: Ural State University Internal Contest October'2000 Junior Session

/**
 *
 * 第一个人第一次取走k%(l+1)后，剩下的button是(l+1)的倍数，这时无论第二个人取几个（设他取i个），第一个下一次都可以取(l+1-i)个，使剩下的button也是(l+1)的倍数。
 *
 */

#include <iostream>
using namespace std;
int main()
{
    int l=3,k;
    cin>>k;
    while(k%l!=0)
        l++;
    cout<<l-1<<endl;
    return 0;
}