POCRI - Power Crisis

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 13 <= N < 100. 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.

Example

Input:
17
0

Output:
7

Added by:Andres Tellez
Date:2011-05-17
Time limit:3.381s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64

hide comments
2020-08-03 23:57:45
what i know is that n is bigger than 100
take 1000 atleast
simple brute force by the way
2020-07-29 09:56:14
my brute force solution is giving me tle pls explain why?

[NG]: Don't post code here; use forum for questions.


Last edit: 2020-07-29 22:37:21
2019-04-18 19:58:12
A rather bland question. Don't think too much, m has a not-so-large upper bound. Go brute-force.
(Proving that m has a not-so-large upper bound is what's interesting).
2016-06-29 18:21:59 Piyush Kumar
I feel there should be some constraint on the source code limit of such questions !

Last edit: 2016-06-29 19:02:32
2015-12-11 06:15:01
@Miguel Angel Diaz, and everyone else who got it accepted on UVa: the test cases on UVa are terribly weak and miss all the interesting ones. For example, the answer for N=84 should be the highest in the specified range - check whether that is the case with your program.
2014-05-12 17:56:17 RIVU DAS
Nice implementation of Josephus problem!!
2014-02-11 23:31:02 Victim
very nice question....
Joshephus problem :)
2013-06-25 20:14:07 Vipul Pandey
a very nice problem.
2013-06-23 18:50:00 Ouditchya Sinha
@Neo : Nice Catch( m can be > N )! AC!! Nice Problem. :)
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