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문제

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.

입력

Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. The first value indicates 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.

출력

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.

예제 입력

4 6
A<B
A<C
B<C
C<D
B<D
A<B
3 2
A<B
B<A
26 1
A<Z
0 0

예제 출력

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

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