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'`.