<p>You are given two strings <code>start</code> and <code>target</code>, both of length <code>n</code>. Each string consists <strong>only</strong> of the characters <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, and <code>&#39;_&#39;</code> where:</p>

<ul>
	<li>The characters <code>&#39;L&#39;</code> and <code>&#39;R&#39;</code> represent pieces, where a piece <code>&#39;L&#39;</code> can move to the <strong>left</strong> only if there is a <strong>blank</strong> space directly to its left, and a piece <code>&#39;R&#39;</code> can move to the <strong>right</strong> only if there is a <strong>blank</strong> space directly to its right.</li>
	<li>The character <code>&#39;_&#39;</code> represents a blank space that can be occupied by <strong>any</strong> of the <code>&#39;L&#39;</code> or <code>&#39;R&#39;</code> pieces.</li>
</ul>

<p>Return <code>true</code> <em>if it is possible to obtain the string</em> <code>target</code><em> by moving the pieces of the string </em><code>start</code><em> <strong>any</strong> number of times</em>. Otherwise, return <code>false</code>.</p>

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

<pre>
<strong>Input:</strong> start = &quot;_L__R__R_&quot;, target = &quot;L______RR&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> We can obtain the string target from start by doing the following moves:
- Move the first piece one step to the left, start becomes equal to &quot;<strong>L</strong>___R__R_&quot;.
- Move the last piece one step to the right, start becomes equal to &quot;L___R___<strong>R</strong>&quot;.
- Move the second piece three steps to the right, start becomes equal to &quot;L______<strong>R</strong>R&quot;.
Since it is possible to get the string target from start, we return true.
</pre>

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

<pre>
<strong>Input:</strong> start = &quot;R_L_&quot;, target = &quot;__LR&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> The &#39;R&#39; piece in the string start can move one step to the right to obtain &quot;_<strong>R</strong>L_&quot;.
After that, no pieces can move anymore, so it is impossible to obtain the string target from start.
</pre>

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

<pre>
<strong>Input:</strong> start = &quot;_R&quot;, target = &quot;R_&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> The piece in the string start can move only to the right, so it is impossible to obtain the string target from start.</pre>

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

<ul>
	<li><code>n == start.length == target.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>start</code> and <code>target</code> consist of the characters <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, and <code>&#39;_&#39;</code>.</li>
</ul>

class Solution:
    def canChange(self, start: str, target: str) -> bool:
        # Since Ls and Rs can move to left and right only respectively, all positions of Ls in start must be no less than the corresponding ones in target, and all positions of Rs in start must be no greater than the corresponding ones in target.
        # return false if start's L count > target's L count(L blocks R) and vice versa
        # so that their relative order must be identical
        s = start.replace("_", "")
        t = target.replace("_", "")
        if s != t:
            return False

        left  = 0 # number of L seen in target but not in start
        right = 0 # number of R seen in start  but not in target
        for a, b in zip(start, target):
            if   a == "L":
                left  -= 1
            elif a == "R":
                right += 1

            if   b == "L":
                left  += 1
            elif b == "R":
                right -= 1

            if left < 0 or right < 0:
                return False

        return True
        
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