By Gustavo Ribeiro, IFPB - Campina Grande Brazil
After having a barbecue to celebrate the results of OPI (Paraíba’s Informatics Olympiad) with his friends, Rerisson wants to have another barbecue, this time a greater one. The goal of this barbecue is to meet new people. He will invite all the persons who have a degree of relationship to him (called g) of at most G. For example, consider ‘>’ as a direct relationship simbol.
Rerisson > Lucas
Rerisson > Jonathan
Lucas > Jonathan
Jonathan > Pedro
Pedro > Juan
Lucas > Juan
For this example, considering G = 1, just Lucas and Jonathan will be invite to the barbecue.
With the help of a social network, Rerisson knows all direct relashionships of everybody, but he’s busy preparing the barbecue. Could you help Rerisson decide which people will be invited to the great party?
The first line of the input will contain two integers, 3 ≤ n ≤ 103 e 1 ≤ G ≤ 500, the quantity of relations to be considered and the maximum relashionship degree, respectively. Each of the next lines will contain two strings S and T, 1 ≤ |S|, |T| ≤ 20 composed by latin american letters only, describing a direct relashionship (The relashionship is mutual).
Print the number of peoples that will be invited to the barbecue, following by their names in ascending lexicografical order.
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