# Sorting It All Out

Time Limit: 1 Second Memory Limit: 32768 KB

An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.## Input

Input consists of multiple problem instances. Each instance starts with a line
containing two positive integers n and m. the first value indicated the number
of objects to sort, where 2 <= n <= 26. The objects to be sorted will
be the first n characters of the uppercase alphabet. The second value m indicates
the number of relations of the form A < B which will be given in this problem
instance. Next will be m lines, each containing one such relation consisting
of three characters: an uppercase letter, the character "<" and
a second uppercase letter. No letter will be outside the range of the first
n letters of the alphabet. Values of n = m = 0 indicate end of input.

## Output

For each problem instance, output consists of one line. This line should be one of the following three:

Sorted sequence determined after xxx relations: yyy...y.

Sorted sequence cannot be determined.

Inconsistency found after xxx relations.

where xxx is the number of relations processed at the time either a sorted
sequence is determined or an inconsistency is found, whichever comes first,
and yyy...y is the sorted, ascending sequence.

## Sample Input

4 6 A A B C B A 3 2 A B 26 1 A 0 0

## Sample Output

Sorted sequence determined after 4 relations: ABCD. Inconsistency found after 2 relations. Sorted sequence cannot be determined.Submit

Source: East Central North America 2001