A sumo tournament is held in Tokyo, in which 2^N sportsmen take part. In each encounter there is a winner, and the loser drops out of the tournament. Thus, in order to determine the winner of the tournament, it is necessary to conduct N rounds.

The organizers wish that in as many rounds as possible all encounters would be held between sumoists from different prefectures of Japan. For that they can forge the drawing results arbitrarily.

The first line contains the number N (1 ≤ N ≤ 10). Each of the next 2^N lines contains the name of a sumouist and the prefecture which he presents. The name and prefecture are sequences of Latin letters of length not exceeding 30.

Output the maximal number of rounds in which sumoists from the same prefecture will not fight each other regardless of the outcomes of encounters (that is, find the maximal possible K such that in at least K rounds all encounters will be between sumoists from different prefectures). The organizers can control the initial arrangement of sportsmen but can't control results of encounters.