Stammering Aliens

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 $m$ ($m \geq 1$), 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 starting position of this
substring.

Sample Input 1 | Sample Output 1 |
---|---|

3 baaaababababbababbab 11 baaaababababbababbab 3 cccccc 0 |
5 12 none 4 2 |