The Postman

Memory limit: 64 MB

Each morning Byteasar the Postman has to visit every street of his district and deliver the mail. All of the roads are one-way and are connected by the (pairwise distinct) crossroads. A pair of crossroads may be connected by two roads at the most: one for each of the opposing directions. The crossroads are numbered from 1 to .

Byteasar starts and ends each route in Byteotian Post headquarters, by the first crossroads. For as long as it can be remembered Byteasar had been choosing his route by himself, but recently the board of directors has issued a new regulation, limiting the freedom of choice of the routes. Each postman has been assigned a collection of route fragments - a set of sequences of crossroads. Byteasar has to choose such a route which:

• leads down each street once only,
• comprises each of the assigned sequences (as a consistent subsequence),
• starts and ends by the first crossroads.

Task

Write a programme which:

• reads from the standard input a description of the streets and assigned sequences,
• verifies if it is possible for Byteasar to get around his district in such a way as to allow him to visit each street exactly once and to fulfill the directors' assigment,
• writes the route found to the standard ouput or concludes that such a route does not exist.

Input

The first line of the standard input contains two integers and separated by a single space, , , denoting the number of crossroads and roads, respectively. The following lines contain the descriptions of the roads: two integers , , separated by a single space, , , denote a one-way road from the crossroads to . Each (ordered) pair appears in the data once at the most. In the following line there is an integer , , denoting the number of assigned sequences. The successive lines contain the descriptions of these sequences. A description consists of an integer , , and a sequence of crossroads' numbers. The numbers in a line are separated by single spaces. The total length of all of the sequences does not exceed .

Ouput

Your programme should write in the first line of the standard output:

• TAK (YES in Polish) - if a route satisfying the requirements of the task exists,
• NIE (NO in Polish) - if such a route does not exist.

• ,
• and (for ) are connected by a street,
• each street appears on the list once only,
• the route comprises, as a consistent subsequence all of the sequences imposed by the board of directors.

6 10
1 5
1 3
4 1
6 4
3 6
3 4
4 3
5 6
6 2
2 1
4
3 1 5 6
3 3 4 3
4 4 3 6 4
3 5 6 2

TAK
1
3
4
3
6
4
1
5
6
2
1

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