Dr. Ellie Arroway has established contact with an extraterrestrial
civilization. However, all efforts to decode their messages have failed so far
because, as luck would have it, they have stumbled upon a race of stuttering
aliens! Her team has found out that, in every long enough message, the most
important words appear repeated a certain number of times as a sequence of
consecutive characters, even in the middle of other words. Furthermore,
sometimes they use contractions in an obscure manner. For example, if they
need to say bab twice, they might just send the message babab, which has
been abbreviated because the second b of the first word can be reused as the
first b of the second one.
Thus, the message contains possibly overlapping repetitions of the same words
over and over again. As a result, Ellie turns to you, S.R. Hadden, for help in
identifying the gist of the message.
Given an integer m, and a string s, representing the message, your task is
to find the longest substring of s that appears at least m times. For
example, in the message
baaaababababbababbab, the length-5 word babab is
contained 3 times, namely at positions 5, 7 and 12 (where indices start
at zero). No substring appearing 3 or more times is longer (see the first
example from the sample input). On the other hand, no substring appears 11
times or more (see example 2).
In case there are several solutions, the substring with the rightmost
occurrence is preferred (see example 3).
The input contains several test cases. Each test case consists of a
line with an integer m (m1), the minimum number of repetitions,
followed by a line containing a string s of length between m and 40 000,
inclusive. All characters in s are lowercase characters from ``a'' to ``z''.
The last test case is denoted by
m = 0 and must not be processed.
Print one line of output for each test case. If there is no solution, output
none; otherwise, print two integers in a line, separated by a space.
The first integer denotes the maximum length of a substring appearing at least
m times; the second integer gives the rightmost possible starting position of such a
substring.
3
baaaababababbababbab
11
baaaababababbababbab
3
cccccc
0
5 12
none
4 2