<p>A <strong>0-indexed</strong> array <code>derived</code> with length <code>n</code> is derived by computing the <strong>bitwise XOR</strong>&nbsp;(&oplus;) of adjacent values in a <strong>binary array</strong> <code>original</code> of length <code>n</code>.</p>

<p>Specifically, for each index <code>i</code> in the range <code>[0, n - 1]</code>:</p>

<ul>
	<li>If <code>i = n - 1</code>, then <code>derived[i] = original[i] &oplus; original[0]</code>.</li>
	<li>Otherwise, <code>derived[i] = original[i] &oplus; original[i + 1]</code>.</li>
</ul>

<p>Given an array <code>derived</code>, your task is to determine whether there exists a <strong>valid binary array</strong> <code>original</code> that could have formed <code>derived</code>.</p>

<p>Return <em><strong>true</strong> if such an array exists or <strong>false</strong> otherwise.</em></p>

<ul>
	<li>A binary array is an array containing only <strong>0&#39;s</strong> and <strong>1&#39;s</strong></li>
</ul>

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

<pre>
<strong>Input:</strong> derived = [1,1,0]
<strong>Output:</strong> true
<strong>Explanation:</strong> A valid original array that gives derived is [0,1,0].
derived[0] = original[0] &oplus; original[1] = 0 &oplus; 1 = 1 
derived[1] = original[1] &oplus; original[2] = 1 &oplus; 0 = 1
derived[2] = original[2] &oplus; original[0] = 0 &oplus; 0 = 0
</pre>

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

<pre>
<strong>Input:</strong> derived = [1,1]
<strong>Output:</strong> true
<strong>Explanation:</strong> A valid original array that gives derived is [0,1].
derived[0] = original[0] &oplus; original[1] = 1
derived[1] = original[1] &oplus; original[0] = 1
</pre>

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

<pre>
<strong>Input:</strong> derived = [1,0]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no valid original array that gives derived.
</pre>

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

<ul>
	<li><code>n == derived.length</code></li>
	<li><code>1 &lt;= n&nbsp;&lt;= 10<sup>5</sup></code></li>
	<li>The values in <code>derived</code>&nbsp;are either <strong>0&#39;s</strong> or <strong>1&#39;s</strong></li>
</ul>

class Solution:
    def doesValidArrayExist(self, derived: List[int]) -> bool:
        res = 0
        for d in derived:
            res ^= d
        return res == 0
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