Ključ - Državno

The Secret Committee has worked hard preparing the tasks for this year's Nationals, and the time has come to send those tasks to the places where the competition will be held. Of course, the tasks are kept as top secret, so they are ecrypted with a well known algorithm in the Secret Committee's labs prior to being sent.

The described algorithm encrypts a text of length N ∙ M in the following manner: a matrix containing N rows and M columns gets filled with letters from the text line by line, downwards. Afterwards, some columns' places are swapped. Formally, the key used for the encryption is a permutation of numbers from 1 to M. We represent the key as a sequence (a₁, a₂ ,... , a_M), where a_i represents the new position of the ith column in the matrix. After applying the key, the encrypted text is read from the matrix in the same order as it was added to the matrix.

Unfortunately, the Committee members are suffering from slight amnesia and they can't recall the key they used for the encryption. Of course, since the Secret Committee is very responsible, a plan was already devised in the event that this happens. In a secret safe, stored in the Secret Committee HQ (the location of which is also secret), they have stored a text with a very important quality - by encrypting that text with any key, no lexicographically greater encrypted text is got than the one encrypted using the forgotten key.

You are given the matrix to be encrypted. Determine the forgotten key.