Design a circuit that allows a user to select between $3$ different sequences. Use ONLY the following devices: AND$/$OR$/$NOT gates, MUX$/$DEMUX$,$ Binary Decoder$/$Encoder$,$ and the positive edge triggered T$-$FF shown below. You may not need all the devices listed.

You are REQUIRED TO MINIMIZE your logic as much as possible.

The first sequence should recycle the following count: $000,001,011,010,110,100.$

The second sequence should recycle the following count: $111,110,101,100,011,010,001,000.$

The third sequence should recycle the following count: $000,111$

$\backslash$table$[[$Input$,$Outputs$],[$PresentState$,$NextState$],[T,Q_n,Q_{n1}$