500 ants are randomly put on a 1-meter stick. Each ant randomly moves toward one end of the stick (right or left with equal probability) at constant speed of 1 meter/minute until it falls off at one end of the stick. If two ants collide, they both immediately change their direction but keep on moving at 1 meter/min (elastic collision).
What is the expected time for all the ants to fall off the stick?