Power Crisis

Problem Description

During the power crisis in New Zealand this winter (caused by a shortage of rain and hence low levels in the hydro dams), a contingency scheme was developed to turn off the power to areas of the country in a systematic,
totally fair, manner. The country was divided up into N regions (Auckland was region number 1, and Wellington number 13). A number, m, would be picked `at random', and the power would first be turned off in region 1
(clearly the fairest starting point) and then in every m'th region after that, wrapping around to 1 after N, and ignoring regions already turned off. For example, if N = 17 and m = 5, power would be turned off to the
regions in the order:1,6,11,16,5,12,2,9,17,10,4,15,14,3,8,13,7. The problem is that it is clearly fairest to turn off Wellington last (after all, that is where the Electricity headquarters are), so for a given
N, the `random' number m needs to be carefully chosen so that region 13 is the last region selected.
Write a program that will read in the number of regions and then determine
the smallest number m that will ensure that Wellington (region 13) can function while the rest of the country is blacked out.

Input

Input will consist of a series of lines, each line containing the number of regions (N) with . The file will be terminated by a line consisting of a single 0.

Output

Output will consist of a series of lines, one for each line of the input. Each line will consist of the number m according to the above scheme.

Sample Input

17
0

Sample Output

7

#include<iostream>
#include<cstdio>
using namespace std;
int a[100000];
int main()
{
	//freopen("a.txt","r",stdin);
	int n;
	while(scanf("%d",&n)!=EOF&&n)
	{
		int i,cnt,k,j;
		for(i=1;;i++)
		{
			k=n; cnt=1;
			for(j=1;j<n;j++)
		     a[j]=j+1;
		    a[n]=2;
			while(a[k]!=k)
		    {
				while(cnt<i)
				{
					k=a[k];
					cnt++;
				}
				a[k]=a[a[k]];
				cnt=1;
		    }
		    if(k==13) {printf("%d\n",i); break;}
		}
	}
	return 0;
}