### Weights and Scale

In Dr. Hong's home gym, there are some unlabeled weights. There is also a simple balancing scale, where he can place the weights in either or both sides of the scale. Dr. Hong comes to a sporting goods shop to buy three labeled weights, so that he can use them together with the simple balancing scale to measure any weights in consecutive integer number of pounds, starting from 1 lb, 2 lb, ..., up to N lb. The labeled weights Dr. Hong can choose from include 1 lb, 2 lb, 3 lb, ..., up to 50 lb. If Dr. Hong cannot use one or more unlabeled weights to measure another unlabeled weight, what is the largest possible value for N?