Vlak
Time limit1sMemory limit512 MB
Two players alternately append letters so the growing word stays a prefix of a word in the mover's own song; decide who wins under optimal play.
- Level
Hard8 of 10
- Topics
- Trie, Game theory, DFS, Tree
- Solved
- No attempts yet
Problem
Nina and Emilija are playing a game on a piece of paper. Initially, the paper is empty. In one move a player appends a letter to the end of the word that is currently written on the paper. They alternate turns, and Nina plays first.
Players must choose the letters in such a way that the following condition is met: the word that is written after the player's move must be a prefix of some word in that player's favourite song. If the player can't make a move, she loses.
If both players play optimally, determine who wins.
Input
The first line contains a positive integer n, the number of words in Nina's favourite song. Each of the following n lines contains a word from Nina's favourite song.
The following line contains a positive integer m, the number of words in Emilija's favourite song. Each of the following m lines contains a word from Emilija's favourite song.
Words in input contain only lowercase letters, and the sum of the lengths of all words is at most 200 000.
Output
Output Nina or Emilija, the name of the winner.
Hint
Clarification of the first example:
If Nina first writes b, Emilija must write b, and then Nina can write b. The current word is bbb, and Emilija can't make a move, so Nina wins.
If Nina would first write a, Emilija could write b. The word would be ab, and Nina wouldn't be able to make a move, and she would lose.