#224EasySimulation· Repeating Instruction Cycle

Robot Patrol Loop

A warehouse robot starts at the origin of an infinite floor, facing north. It is given a patrol program, a string of commands, and repeats the whole program forever: - `G`: move one cell forward in the current direction. - `L`: turn 90 degrees left in place. - `R`: turn 90 degrees right in place. The robot is **contained** if there is some circle on the floor that it never leaves, no matter how many times the program repeats. Return `true` when the robot stays contained and `false` when it drifts away without bound.

Input format

`instructions`: a string made of the characters G, L and R.

Output format

A boolean.

Examples

Input: instructions = "GGLLGG"

Output: true

The robot goes two cells north, turns around and walks two cells back to the origin, now facing south. A second pass retraces the same line and returns it to the origin facing north again, so it never leaves a small area.

Input: instructions = "GG"

Output: false

It walks north forever, so it is not contained.

Input: instructions = "GL"

Output: true

One step then a left turn: after four repetitions the robot walks a square and is back at the origin.

Constraints

1 <= instructions.length <= 100
instructions[i] is one of G, L, R.

#simulation
#math
#geometry
#strings