Construct a finite$-$state machine that models a newspaper vending machine that accepts $$5,$ $$10$ and $$20$ coins.$$ The machine has an automatic locking door $($D$)$ that is unlocked only after $$30$ or more have been inserted.$$ Once the door is unlocked the customer opens it and takes a paper, and closes the door.$$ No change is ever returned no matter how much extra money has been inserted.$$ The next customer starts with no credit.$$ While the door has not been opened, the customer may press a red cancel button $($C$)$ to cancel the purchase and have all collected money returned.

By representing the finite$-$state machine as a state diagram,

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Assuming:

$1.$ There are No parallel edges i$.$e$.$ where more than one transition occurs between two states $($and more than one edges could have been drawn$),$ a single edge is drawn and the multiple input$-$output labels are placed on that edge

$2.$ Following from the previous point, there are No parallel loops i$.$e$.$ where more than one transition occurs from a single state $($and more than one loops could have been drawn to the single state$),$ a single loop is drawn and the multiple input$-$output labels are placed on that loop

State the number of edges $($including loops$)$ to be seen within the state diagram where THE INPUT Section of the LABEL reflects $5,10$ or $20$ and THE OUTPUT Section of the LABEL reflects an output greater than $"$n$".$