Description

An ascending sorted sequence of distinct values is a sequence whose elements strictly increase from left to right. For example, an ordered sequence $A, B, C, D$ means $A < B$, $B < C$, $C < D$. In this problem, you are given a series of relations of the form $A < B$, and you are asked to determine whether these relations are sufficient to determine the order of the sequence.

Input Format

The first line contains two positive integers $n$ and $m$. Here, $n$ is the number of elements to sort, $2 \leq n \leq 26$. The $1$-st to the $n$-th elements are represented by uppercase letters $A, B, C, D, \dots$. The integer $m$ is the number of relations of the form $A < B$.

The next $m$ lines each contain exactly $3$ characters: an uppercase letter, the character <, and another uppercase letter, representing a relation between two elements.

Output Format

If the first $x$ relations are sufficient to determine the order of the $n$ elements yyy...y (e.g., ABC), output

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

Here, $x$ means the number of relations considered (the first $x$ relations).

If a contradiction is detected within the first $x$ relations (e.g., $A < B$, $B < C$, $C < A$), output

Inconsistency found after x relations.

Here, $x$ has the same meaning as above.

If the order of the $n$ elements cannot be determined after all $m$ relations, output

Sorted sequence cannot be determined.

(Hint: Once the order of the $n$ elements is determined, you can terminate the program immediately. You do not need to consider contradictions that may appear after that.)

Input Format

Output Format

4 6
A<B
A<C
B<C
C<D
B<D
A<B

Sorted sequence determined after 4 relations: ABCD.

3 2
A<B
B<A

Inconsistency found after 2 relations.

26 1
A<Z

Sorted sequence cannot be determined.

Hint

$2 \leq n \leq 26, 1 \leq m \leq 600$.

Translated by ChatGPT 5