A mobile is a type of kinetic sculpture constructed to take
advantage of the principle of equilibrium. It consists of a
number of rods, from which weighted objects or further rods
hang. The objects hanging from the rods balance each other, so
that the rods remain more or less horizontal. Each rod hangs
from only one string, which gives it freedom to rotate about
the string.
We consider mobiles where each rod is attached to its string
exactly in the middle, as in the figure underneath. You are
given such a configuration, but the weights on the ends are
chosen incorrectly, so that the mobile is not in equilibrium.
Since thatâ€™s not aesthetically pleasing, you decide to change
some of the weights.
What is the minimum number of weights that you must change
in order to bring the mobile to equilibrium? You may substitute
any weight by any (possibly noninteger) weight. For the mobile
shown in the figure, equilibrium can be reached by changing the
middle weight from 7 to 3, so only 1 weight needs to
changed.
Input
On the first line one positive number: the number of
testcases, at most 100. After that per testcase:

One line with the structure of the mobile, which is a
recursively defined expression of the form:
\[ \langle
\texttt{expr}\rangle \; \; ::= \; \; \langle
\texttt{weight}\rangle \; \; \mid \; \; \mbox{``[''} \;
\langle \texttt{expr}\rangle \; \mbox{``,''} \; \langle
\texttt{expr}\rangle \; \mbox{``]''} \]
with $\langle
\texttt{weight}\rangle $ a positive integer smaller
than $10^9$ indicating
a weight and $[\langle
\texttt{expr}\rangle ,\langle \texttt{expr}\rangle
]$ indicating a rod with the two expressions at the
ends of the rod. The total number of rods in the chain from
a weight to the top of the mobile will be at most 16.
Output
Per testcase:
Sample Input 1 
Sample Output 1 
3
[[3,7],6]
40
[[2,3],[4,5]]

1
0
3
