The TAs have come together to build an aviary for endangered birds. It is a cubic room that measures 10 meters by 10 meters by 10 meters. Inside the aviary are nine brightly colored exotic birds that are all free to fly about the room. However, Alex comes and argues that the room is too small for so many birds, and that at any given moment, there are at least two birds that are no more than 53 meters apart. Prove Alex's statement so that the birds may receive a larger home. (Hint: Remember that the pythagorean theorem tells us that the length of the hypotenuse of a triangle is the square root of the sum of (1) the square of the length of one leg of the triangle and (2) the square of the length of the other leg of the triangle!)