github.com/captn3m0/codechef.git

---
category_name: easy
problem_code: BINIM
problem_name: 'Binary Nim'
languages_supported:
    - C
    - CPP14
    - JAVA
    - PYTH
    - 'PYTH 3.5'
    - 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
max_timelimit: '1'
source_sizelimit: '50000'
problem_author: alei
problem_tester: null
date_added: 15-04-2018
tags:
    - alei
    - combinatorial
    - cook93
    - game
    - game
    - greedy
    - nim
editorial_url: 'https://discuss.codechef.com/problems/BINIM'
time:
    view_start_date: 1524421800
    submit_start_date: 1524421800
    visible_start_date: 1524421800
    end_date: 1735669800
    current: 1525198933
is_direct_submittable: false
layout: problem
---
All submissions for this problem are available.### Read problem statement in [Mandarin chinese](http://www.codechef.com/download/translated/COOK93/mandarin/BINIM.pdf) and [Vietnamese](http://www.codechef.com/download/translated/COOK93/vietnamese/BINIM.pdf).

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 ```