<image>The electronic flea game board is the triangle △ABC as shown in the image. Given AB=8, AC=9, and BC=10. If the flea starts at point P on side BC, where BP=4. The flea's first jump is from P to P_{1} on side AC (first landing point), with CP_{1}=CP. The second jump is from P_{1} to P_{2} on side AB (second landing point), with AP_{2}=AP_{1}. The third jump is from P_{2} to P_{3} on side BC (third landing point), with BP_{3}=BP_{2}. The flea continues jumping following this rule. If P_{n} (P_{n} is the nth landing point, where n is a positive integer), then the distance between P_{2010} and C is ___ 
