# Amazon Online Assessment 2021 (OA) - Robot Bounded in Circle

On an infinite plane, a robot is programmed to repeat a set of movements indefinitely. The robot starts at position `(0, 0)` facing north. The movement can be one of three:

• `"S"`: go straight 1 unit
• `"L"`: turn 90 degrees to the left
• `"R"`: turn 90 degrees to the right

Find out if there exists a circle in the plane such that the robot never leaves the circle.

### Input

`movements`: a string made up of 'S', 'L', 'R' that determines the robot's future position on the plane.

### Output

Return `true` if the robot is bounded in a circle in the plane; otherwise return `false`.

### Constraints

• `1 <= movements.length <= 100`

### Examples

#### Example 1:

##### Explanation:

The robot moves from (0, 0) to (0, 2), turns 180 degrees to face south, and then returns to (0, 0). The robot remains in the circle of radius 2 centered at the origin at all times.

#### Example 2:

##### Explanation:

The robot moves north indefinitely.

#### Example 3:

##### Explanation:

The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ..., circling around the perimeter of a square of size 1 on the plane.

## Title

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