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: "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: "GG"
Output: false
Explanation:
The robot moves north indefinitely.
Example 3:
Input: "GL"
Output: true
Explanation:
The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...
Note:
1 <= instructions.length <= 100instructions[i] is in {'G', 'L', 'R'}