Circle Of Fifths

I might have mentioned this before but I hope to reconstruct
the circle of fifths buy noting an arrangement of chords one
can note on paper starting with key of C chords.

CEG  Key of C has no sharps but note 
     last two notes are F and G, 
     Key of G has an F#s
GBD  Key of D has C and F#s
DFA  Key of A has G C and F#s
ACE  Key of E has D G C and F#s 
EGB  Key of B has A D G C and F#s
BDF# Key of F# has E A D G C and F#s HWWW rule (BDF is HWWH)

the arranegment has started flat b notations into rarely used
keys for my use.