B'Andi and Budi were given an assignment to tidy up their bookshelf of n books. Each book is represented by the book title -- a string s_i numbered from 1 to n , each with length m . Andi really wants to sort the book lexicographically ascending, while Budi wants to sort it lexicographically descending. Settling their fight, they decided to combine their idea and sort it asc-desc-endingly, where the odd-indexed characters will be compared ascendingly, and the even-indexed characters will be compared descendingly. A string a occurs before a string b in asc-desc-ending order if and only if in the first position where a and b differ, the following holds: The first line contains two integers n and m ( 1 <= q n cdot m <= q 10^6 ). The i -th of the next n lines contains a string s_i consisting of m uppercase Latin letters -- the book title. The strings are pairwise distinct. Output n integers -- the indices of the strings after they are sorted asc-desc-endingly. The following illustrates the first example. '...