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Walk to the right until you reach the first elevator. The platform will disappear above it. Wait here until the Cube goes back to the left. Take the elevator up and walk to the right until the rightmost platform disappears. You'll fall onto another elevator. Use it and hit the flashing brick when you reach the top. Walk back to the left and use the first elevator again. Press again and it will continue up. Walk onto the rightmost platform and it will disappear, allowing you access to the elevator right below. Take it to the top and walk to the right until you reach the elevator. Destroy the flashing bricks and use the elevators ahead to get to the top. This next part is a little tricky.
Duck under the Cube ahead and stay there until the other one goes by. Now quickly jump over the all of the platforms that are lower than the others. The reason being is that you'll fall through and have to start over again. When you reach the far right, jump onto the elevator and take it up. Stay here until the Cube from the left passes by and then start walking to the right again. Stay on the lowest platforms to avoid getting hit by it. Use the elevator at the far right. Duck under the two Cubes bouncing around and use the third elevator to reach the top. Walk to the right and you'll eventually find a platform that will disappear. You'll fall through a series of them and land on a elevator. Use it to reach the door you saw earlier to finish the stage.