On an infinite plane, a robot initially stands at (0, 0) and faces north. Note that:

The north direction is the positive direction of the y-axis.
The south direction is the negative direction of the y-axis.
The east direction is the positive direction of the x-axis.
The west direction is the negative direction of the x-axis.

The robot can receive one of three instructions:

"G": go straight 1 unit.
"L": turn 90 degrees to the left (i.e., anti-clockwise direction).
"R": turn 90 degrees to the right (i.e., clockwise direction).

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 is initially at (0, 0) facing the north direction. "G": move one step. Position: (0, 1). Direction: North. "G": move one step. Position: (0, 2). Direction: North. "L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: West. "L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: South. "G": move one step. Position: (0, 1). Direction: South. "G": move one step. Position: (0, 0). Direction: South. Repeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (0, 2) --> (0, 1) --> (0, 0). Based on that, we return true.

Example 2:

Input: instructions = "GG" Output: false Explanation: The robot is initially at (0, 0) facing the north direction. "G": move one step. Position: (0, 1). Direction: North. "G": move one step. Position: (0, 2). Direction: North. Repeating the instructions, keeps advancing in the north direction and does not go into cycles. Based on that, we return false.

Example 3:

Input: instructions = "GL" Output: true Explanation: The robot is initially at (0, 0) facing the north direction. "G": move one step. Position: (0, 1). Direction: North. "L": turn 90 degrees anti-clockwise. Position: (0, 1). Direction: West. "G": move one step. Position: (-1, 1). Direction: West. "L": turn 90 degrees anti-clockwise. Position: (-1, 1). Direction: South. "G": move one step. Position: (-1, 0). Direction: South. "L": turn 90 degrees anti-clockwise. Position: (-1, 0). Direction: East. "G": move one step. Position: (0, 0). Direction: East. "L": turn 90 degrees anti-clockwise. Position: (0, 0). Direction: North. Repeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (-1, 1) --> (-1, 0) --> (0, 0). Based on that, we return true.

  Constraints:

1 <= instructions.length <= 100
instructions[i] is 'G', 'L' or, 'R'.