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Read problem statement in Mandarin chinese and Vietnamese.Tweedle-Dee and Tweedle-Dum are playing a fierce match of binary Nim. This novel game is played with $N$ stacks, each of them containing only $1$-s and $0$-s. Just like in normal Nim, Tweedle-Dee and Tweedle-Dum alternate turns; in their turn, a player must choose one non-empty stack and remove a positive number of elements from the top of this stack. However, Tweedle-Dee may only choose a stack with $0$ at the top (and remove elements from it afterwards), and similarly, Tweedle-Dum may only choose a stack with $1$ at the top. the player that cannot make a move loses Suzumo does not want to wait for the end of the game, so given the starting player he asks you to determine the winner. Remember that Tweedle-Dee and Tweedle-Dum are legendary grandmasters of combinatorial games, so both always play optimally. ### Input - The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows. - The first line of each test case contains an integer $N$, a string $S$ denoting the number of stacks, the player that starts the game, respectively. - Each of the following $N$ lines contains a single binary string $B$ representing a stack; the first character of $B$ corresponds to the top element of the stack and the last character to the bottom element. ### Output For each test case, print a single line containing the string `"Dee"` if Tweedle-Dee wins the match or `"Dum"` if Tweedle-Dum wins. ### Constraints - $1 \le T \le 500$ - $1 \le N \le 50$ - $1 \le |B| \le 50$ - each character in $B$ is either '1' or '0' - $S$ is either `"Dee"` or `"Dum"` ### Example Input ``` 2 2 Dee 101 010 2 Dum 101 010 ``` ### Example Output ``` Dum Dee ```
|Tags||alei, combinatorial, cook93, game, game-theory, greedy, nim|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS|
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