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

<ul>
	<li>The <strong>north direction</strong> is the positive direction of the y-axis.</li>
	<li>The <strong>south direction</strong> is the negative direction of the y-axis.</li>
	<li>The <strong>east direction</strong> is the positive direction of the x-axis.</li>
	<li>The <strong>west direction</strong> is the negative direction of the x-axis.</li>
</ul>

<p>The robot can receive one of three instructions:</p>

<ul>
	<li><code>&quot;G&quot;</code>: go straight 1 unit.</li>
	<li><code>&quot;L&quot;</code>: turn 90 degrees to the left (i.e., anti-clockwise direction).</li>
	<li><code>&quot;R&quot;</code>: turn 90 degrees to the right (i.e., clockwise direction).</li>
</ul>

<p>The robot performs the <code>instructions</code> given in order, and repeats them forever.</p>

<p>Return <code>true</code> if and only if there exists a circle in the plane such that the robot never leaves the circle.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> instructions = &quot;GGLLGG&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> The robot is initially at (0, 0) facing the north direction.
&quot;G&quot;: move one step. Position: (0, 1). Direction: North.
&quot;G&quot;: move one step. Position: (0, 2). Direction: North.
&quot;L&quot;: turn 90 degrees anti-clockwise. Position: (0, 2). Direction: West.
&quot;L&quot;: turn 90 degrees anti-clockwise. Position: (0, 2). Direction: South.
&quot;G&quot;: move one step. Position: (0, 1). Direction: South.
&quot;G&quot;: move one step. Position: (0, 0). Direction: South.
Repeating the instructions, the robot goes into the cycle: (0, 0) --&gt; (0, 1) --&gt; (0, 2) --&gt; (0, 1) --&gt; (0, 0).
Based on that, we return true.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> instructions = &quot;GG&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> The robot is initially at (0, 0) facing the north direction.
&quot;G&quot;: move one step. Position: (0, 1). Direction: North.
&quot;G&quot;: 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.
</pre>

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= instructions.length &lt;= 100</code></li>
	<li><code>instructions[i]</code> is <code>&#39;G&#39;</code>, <code>&#39;L&#39;</code> or, <code>&#39;R&#39;</code>.</li>
</ul>

class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        dirction = [(0,1), (-1,0), (0,-1), (1,0)]
        x,y = 0,0
        face = 0

        for instruction in instructions:
            if instruction == "G":
                x += dirction[face][0]
                y += dirction[face][1]
            if instruction == "L":
                face = (face + 1) % 4

            if instruction == "R":
                face = (face -1) % 4

        if (x == 0 and y == 0) or face != 0:
            return True
        else : 
            return False 
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