On an infinite plane, a robot initially stands at (0, 0) and faces north. The robot can receive one of three instructions:
"G": go straight 1 unit;"L": turn 90 degrees to the left;"R": turn 90 degrees to the right.
The robot performs the instructions given in order, and repeats them forever.
Return true if and only if there exists a circle in the plane such that the robot never leaves the circle.
Example 1:
Input: instructions = "GGLLGG" Output: true Explanation: The robot moves from (0,0) to (0,2), turns 180 degrees, and then returns to (0,0). When repeating these instructions, the robot remains in the circle of radius 2 centered at the origin.
Example 2:
Input: instructions = "GG" Output: false Explanation: The robot moves north indefinitely.
Example 3:
Input: instructions = "GL" Output: true Explanation: The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...
Constraints:
1 <= instructions.length <= 100instructions[i]is'G','L'or,'R'.