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+500 ants are placed on a 1-foot string without any order. Assume independent uniform distribution for each ant. 
+Each ant will move randomly towards either end of the string at a constant speed of 1 foot per minute. 
+The ants will keep moving until they reach the end of the string, and if two ants collide head-on, they will both immediately turn around and continue moving.
+Assuming that the size of the ants is infinitely small, what is the expected time for all 500 ants to fall off the string?