P3546 [POI 2012] PRE-Prefixuffix

We consider strings consisting of lowercase letters of the English alphabet in this problem. An initial fragment of a given string is called its prefix. A final (terminal) fragment of a given string is called its suffix. In particular, the empty string is both a prefix and a suffix of any string. Two strings are cyclically equivalent if one of them can be obtained from another by moving its certain suffix from the end of the string to its beginning. For example, the strings  and  are cyclically equivalent, whereas the strings  and  are not. In particular, every string is cyclically equivalent to itself. A string  consisting of  letters is given. We are looking for its prefix  and suffix  of equal length such that:  and  are cyclically equivalent, the common length of  and  does not exceed  (i.e., the prefix  and the suffix  do not overlap in ), and the common length of  and  is maximized. 对于两个串 $S_1, S_2$，如果能够将 $S_1$ 的一个后缀移动到开头后变成 $S_2$，就称 $S_1$ 和 $S_2$ 循环相同。例如串 ababba 和串 abbaab 是循环相同的。 给出一个长度为 $n$ 的串 $S$，求满足下面条件的最大的 $L(L\leq \frac n 2)$：$S$ 的 $L$ 前缀和 $S$ 的 $L$ 后缀是循环相同的。

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数据范围： - 对于 $30\%$ 的数据，保证 $n\le 500$； - 对于 $50\%$ 的数据，保证 $n\le 5000$； - 对于 $100\%$ 数据，保证 $1\le n\le 10^6$。