<p>Given a string <code>path</code>, where <code>path[i] = &#39;N&#39;</code>, <code>&#39;S&#39;</code>, <code>&#39;E&#39;</code> or <code>&#39;W&#39;</code>, each representing moving one unit north, south, east, or west, respectively. You start at the origin <code>(0, 0)</code> on a 2D plane and walk on the path specified by <code>path</code>.</p>

<p>Return <code>true</code> <em>if the path crosses itself at any point, that is, if at any time you are on a location you have previously visited</em>. Return <code>false</code> otherwise.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/10/screen-shot-2020-06-10-at-123929-pm.png" style="width: 400px; height: 358px;" />
<pre>
<strong>Input:</strong> path = &quot;NES&quot;
<strong>Output:</strong> false 
<strong>Explanation:</strong> Notice that the path doesn&#39;t cross any point more than once.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/10/screen-shot-2020-06-10-at-123843-pm.png" style="width: 400px; height: 339px;" />
<pre>
<strong>Input:</strong> path = &quot;NESWW&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> Notice that the path visits the origin twice.</pre>

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

<ul>
	<li><code>1 &lt;= path.length &lt;= 10<sup>4</sup></code></li>
	<li><code>path[i]</code> is either <code>&#39;N&#39;</code>, <code>&#39;S&#39;</code>, <code>&#39;E&#39;</code>, or <code>&#39;W&#39;</code>.</li>
</ul>

class Solution:
    def isPathCrossing(self, path: str) -> bool:
        d = {
            "N": (0, 1), 
            "S": (0, -1), 
            "E": (1, 0), 
            "W": (-1, 0)
        }.__getitem__
        x = y = 0
        vis = {(0, 0)}
        for dx, dy in map(d, path):
            x += dx
            y += dy
            pos = (x, y)
            if pos in vis: return True
            vis.add(pos)
        return False
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