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 length5 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).
Input
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.
Output
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
