Prince and the Dragon

Prince Charles went to fight a 3 headed, 3 tailed dragon.

He has a magic sword. 

In one stroke it can chop of either * one head, * two heads,* one tail or  

two tails *. 

The dragon is a type , if one head is chopped off, new head grows  

If one tail is chopped off, two tails grow

If two tails are chopped off, one new head would grow   

If two heads are chopped off, nothing grows
What is the minimum number of strokes required to chop off


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