<p>There is an integer array <code>perm</code> that is a permutation of the first <code>n</code> positive integers, where <code>n</code> is always <strong>odd</strong>.</p>

<p>It was encoded into another integer array <code>encoded</code> of length <code>n - 1</code>, such that <code>encoded[i] = perm[i] XOR perm[i + 1]</code>. For example, if <code>perm = [1,3,2]</code>, then <code>encoded = [2,1]</code>.</p>

<p>Given the <code>encoded</code> array, return <em>the original array</em> <code>perm</code>. It is guaranteed that the answer exists and is unique.</p>

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

<pre>
<strong>Input:</strong> encoded = [3,1]
<strong>Output:</strong> [1,2,3]
<strong>Explanation:</strong> If perm = [1,2,3], then encoded = [1 XOR 2,2 XOR 3] = [3,1]
</pre>

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

<pre>
<strong>Input:</strong> encoded = [6,5,4,6]
<strong>Output:</strong> [2,4,1,5,3]
</pre>

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

<ul>
	<li><code>3 &lt;= n &lt;&nbsp;10<sup>5</sup></code></li>
	<li><code>n</code>&nbsp;is odd.</li>
	<li><code>encoded.length == n - 1</code></li>
</ul>

class Solution:
    def decode(self, encoded: List[int]) -> List[int]:
        n = len(encoded) + 1
        perm = [0] * n
        total_xor = 0
        
        for i in range(1, n + 1):
            total_xor ^= i
        
        xor_encoded = 0
        for i in range(1, n - 1, 2):
            xor_encoded ^= encoded[i]
        
        perm[0] = total_xor ^ xor_encoded
        
        for i in range(1, n):
            perm[i] = perm[i - 1] ^ encoded[i - 1]
        
        return perm

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