Mixing Colours

Frank lives in London and he really likes games and maths. Lately, he has been playing a game on his mobile phone. It is simple, a sequence of coloured tokens is provided and each turn the player has to combine a pair of adjacent tokens to obtain a new token of certain colour. This process is repeated until the whole sequence results in only one final token. The problem is that not every pair of colours can be merged. There is a set of rules describing the allowed combinations. For example, given the following rules

\begin{equation*} \begin{matrix} \text {blue} & + & \text {yellow} & \to & \text {green} \\ \text {yellow} & + & \text {red} & \to & \text {orange} \\ \text {blue} & + & \text {orange} & \to & \text {brown} \\ \end{matrix}\end{equation*}and the sequence (blue, yellow, red), the game could be
finished obtaining a `brown` token
after two steps: $(\mathtt{blue},
\mathtt{yellow}, \mathtt{red}) \to (\mathtt{blue},
\mathtt{orange}) \to (\mathtt{brown})$.

Frank is now in Valencia attending a famous programming
contest and he is waiting for the tram to go to the university.
Meanwhile, he is playing this game to fill time but the sun is
shining so bright that he can not properly see the screen of
his phone. He has some certainty about the possible colour of
each token and he is wondering what will be the resulting
colour following the most likely play of the game according to
his estimation of the input sequence. Given Frank’s estimation
of two colours `A` and `B`, and the combination $\texttt{A} + \texttt{B} \to
\texttt{C}$, the certainty of the obtained colour
`C` is computed as $\mathsf{cer}(\mathtt{C}) =
\mathsf{cer}(\mathtt{A}) \cdot
\mathsf{cer}(\mathtt{B})$.

The first line contains $R$ ($0
< R \leq 100$) the number of rules describing the
allowed combinations of colours. Each of the following
$R$ lines contains three
strings $s_1$,
$s_2$, $s_3$ representing the combination
$s_1 + s_2 \to s_3$. Next
line shows the number of test cases $T$. For each test case an integer
$C$ indicates the length
of the input sequence of tokens ($0 < C \leq 500$). Each of the next
$C$ lines describes a
token, it contains a list of pairs $(k, \mathsf{cer}(k))$ providing a
colour $k$ and its
corresponding certainty ($0 <
\textsf{cer}(k) \leq 1.0$). The list ends with the word
`END`. The sum of the certainties for a
certain token always is $1.0$. Every colour in a test case has
appeared first in the rules describing the game.

For each test case, print the resulting colour of the most
likely play of the game. If there is no possible combination to
finish the game then print `GAMEOVER`.

Sample Input 1 | Sample Output 1 |
---|---|

7 Blue Yellow Green Yellow Red Orange Green Red Yellow White Red Pink Pink Black Red Orange Red Red Yellow Orange Yellow 3 2 Red 0.7 Orange 0.3 END Yellow 1.0 END 4 Blue 0.6 Green 0.4 END Red 0.2 Orange 0.6 Yellow 0.2 END White 0.9 Yellow 0.1 END Red 0.5 Black 0.5 END 2 Blue 1.0 END Orange 1.0 END |
Orange Yellow GAMEOVER |