Description

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

Sample Output

題意

依序給出一些字母之間的大小關(guān)系，判斷并輸出它能否唯一確定一個序列滿足這一關(guān)系。

思路

依舊是一道拓撲排序的題目。

無法唯一確定一個序列當(dāng)且僅當(dāng)在所有關(guān)系輸入完畢之后，進行拓撲排序的時候存在一個以上入度為0的點。

序列不存在會在圖中存在環(huán)的情況下出現(xiàn)。

于是，每輸入一組關(guān)系，進行一次拓撲排序，對此次拓撲排序的結(jié)果判斷并做出相應(yīng)的選擇。

AC 代碼