Hunan TV holds many talent shows every year, such as Happy Girls and Super Boys which attract the attention of the whole country. This year Hunan University held a new type of talent show called Brilliant Programmers. Millions of programmers had registered online and only top N most brilliant programmers got the opportunity to compete on site. The organizer had hold ten rounds of qualification contest and programmers were ranked by their total scores. The programmers who ranked after N were eliminated.
The final show continued for a very long time. Initially programmers were ranked by their qualification scores. The rule was special: A challenge may be happen between exactly two adjacent ranked programmers at any time and the lower ranked one tries to solve the other’s problem. If the challenger successfully solves this problem, their ranks exchange. Otherwise their ranks remain unchanged. It is guaranteed that a programmer never involved in two challenges at the same time. The top ranked programmer at last is the champion.
The show was over but… The hard disk which logs the whole progress was burned out. After data rescue, the number of successful challenges of each programmer was recovered but the final rank was disappeared forever. During the rescue some errors may occur, which lead to some wrong recovered numbers. Is the show possible at all? If it is possible, can you help to find the champion from the very limited information?