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.
The input will consist of a series of lines, each line containing the number of regions (N) with 13 ≤ N < 100. The input will be terminated by a line containing a single 0.
For each line of input, output one line containing the number m according to the above scheme.
Output for Sample Input
|University of Debrecen; Faculty of Informatics; v. 05/24/2018|