There is an integer array perm that represents a permutation of the first $n$ positive integers from $1$ to $n$.

This array was transformed into an integer array encoded of length $n - 1$, where encoded[i] = perm[i] XOR perm[i + 1] for each $i$ ($0 \leq i < n - 1$).

Given the array encoded, reconstruct and return the original array perm. It is guaranteed that the answer exists and is unique.

Constraints:

• $3 \leq n < 10^5$

• $n$ is odd.

• encoded.length $= n - 1$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.