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A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:

$\begin{array}{|c|c|c|} \hline \\  \text{Activity} & \text{Immediate Predecessor} & \text{Estimated duration (weeks)} \\ \hline P & – & 5 \\ \hline Q & – & 1 \\  \hline R & Q & 2 \\ \hline S & P, R & 4 \\ \hline T & P & 6 \\ \hline U & S, T & 3 \\ \hline \end{array}$

If all activities other than $S$ take the estimated amount of time, the maximum duration (in weeks) of the activity $S$ without delaying the completion of the project is ________
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