robotWalk

A robot is standing at the (0, 0) point of the Cartesian plane and is oriented towards the vertical (y) axis in the direction of increasing yvalues (in other words, he’s facing up, or north). The robot executes several commands each of which is a single positive integer. When the robot is given a positive integer Kit moves K squares forward and then turns 90 degrees clockwise.

The commands are such that both of the robot’s coordinates stay non-negative.

Determine if there is a square that the robot visits at least twice after executing all the commands.

Example

• For a = [4, 4, 3, 2, 2, 3], the output should be
  robotWalk(a) = true.

      The path of the robot looks like this:

     The point (4, 3) is visited twice, so the answer is true.

Input/Output

• [execution time limit] 2 seconds (py)

• [input] array.integer a

  An array of positive integers, each number representing a command.

  Guaranteed constraints:
  3 ≤ a.length ≤ 10,
  1 ≤ a[i] ≤ 105.

• [output] boolean

  true if there is a square that the robot visits at least twice, false otherwise.