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 degress 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 <= 100
instructions[i] is in {'G', 'L', 'R'}
class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        move = {'N':(0,1), 'S':(0,-1), 'E':(1,0), 'W':(-1,0)}
        right = {'N':'E', 'S':'W', 'E':'S', 'W':'N'}
        left = {'N':'W', 'S':'E', 'E':'N', 'W':'S'}
        
        pos = (0,0)
        dire = 'N'
        i=0
        while i<4:
            for c in instructions:
                if c=='G':
                    x, y = pos
                    dx, dy = move[dire]
                    pos = (x+dx, y+dy)
                elif c=='L':
                    dire = left[dire]
                else:
                    dire = right[dire]
            
            if pos==(0,0) and dire=='N':
                return True
        
            i+=1
        
        return False
class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        move = {'N':(0,1), 'S':(0,-1), 'E':(1,0), 'W':(-1,0)}
        right = {'N':'E', 'S':'W', 'E':'S', 'W':'N'}
        left = {'N':'W', 'S':'E', 'E':'N', 'W':'S'}
        
        pos = (0,0)
        dire = 'N'
        i=0
        while i<4:
            for c in instructions:
                if c=='G':
                    x, y = pos
                    dx, dy = move[dire]
                    pos = (x+dx, y+dy)
                elif c=='L':
                    dire = left[dire]
                else:
                    dire = right[dire]
            
            if pos==(0,0) and dire=='N':
                return True
        
            i+=1
        
        return False