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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<B

A<C

B<C

C<D

B<D

A<B

3 2

A<B

B<A

26 1

A<Z

0 0

 

Sample Output

Sorted sequence determined after 4 relations: ABCD.

Inconsistency found after 2 relations.

Sorted sequence cannot be determined.

题意： 

这个题就是让判断给出的字母的顺序，如果给出的关系中判断出存在环（回路），比如A<B,B<A。那么输出“Inconsistency found after x  relations.”即在第x个关系之后判断出来存在环；如果给出的关系都无法判断字母的次序，那么就输出“Sorted sequence cannot be determined.”；如果在第x个关系之后就找出了字母的次序，那么就输出“Sorted sequence determined after x relations: （字母的次序）.”。

所以每次输入一个关系就要去进行一次拓扑排序，来判断是否有结果。

代码：

#include
   
    #include
    
     #include
     
      #include
      
       #define maxn 36int path[maxn][maxn];  //例 A
       B 用此数组来记录 int res[maxn];  //记录最终的字母次序 int rudu[maxn];   //每个点的入度int changedu[maxn];char str[8];int n,m; int tuopo(){	for(int i=0;i
        
         1)flag=0;//现在为止存在多个度为0的点，次序暂时不能判断，要继续输入关系。 changedu[k]--; res[count++]=k; //将度为0的点存入数组中 for(int j=0;j
        
      
     
    
   

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