Robot route

A robot is initially in the square (0,0). The robot then moves step by step according to a given sequence of commands. The sequence consists of the symbols U (up), D (down), L (left) and R (right). How many distinct squares does the robot visit?

You may assume that the sequence contains at most 10^5 commands.

In a file robot.py, implement a function count that is given the sequence of commands and returns the number of distinct squares.

def count(s):
    # TODO

if __name__ == "__main__":
    print(count("LL")) # 3
    print(count("UUDLRR")) # 5
    print(count("UDUDUDU")) # 2