The regular decagon $ABCDEFGHIJ$ has its center at $K$. Each of the vertices and the center are to be associated with one of the digits $1$ through $11$, with each digit used once, in such a way that the sums of the numbers on the lines $AKF$, $BLG$, $CMH$, $DNI$, and $EJO$ are all equal. In how many ways can this be done?

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