At the end of the array, you can only achieve xor of any subarray of the original array.
proofLets denote $$$f(u,v) =$$$ xor of all $$$a_i$$$ such that $$$min(u,v) \leq i < max(u,v)$$$. In the first operation you add $$$f(n,i)$$$. I.e. $$$[u_1,v_1)=[n,i)$$$. It can be proven that $$$f(u_k,v_k) = f(v_{k-1},v_k)$$$ in the $$$k$$$-th operation which is a range.
proofSuppose we have taken $$$k$$$ ranges that already satisfy this property. Now, I add a new $$$k+1$$$-th range. So, first I need to take the $$$k$$$-th range $$$f(u_k,v_k)$$$. Now I'm xoring it with the range $$$f(u_{k - 1}, v_{k - 1})$$$. As [ $$$u_k, v_k$$$) and [ $$$u_{k - 1}, v_{k - 1}$$$) share an endpoint, the result for these ranges will be a range.
proofFor two ranges $$$f(x,y)$$$ and $$$f(y,z)$$$, if the two ranges do not intersect, the result will be the sum of the two ranges $$$f(x,z)$$$. If the two ranges intersect, then the intersections will be cancelled out, and the result will be the difference $$$f(x,z)$$$.
Now, we maintain a boolean array $$$b$$$ where $$$b_i$$$ is $$$1$$$ if there is some $$$j$$$ such that $$$a_1 \oplus a_2 \oplus \cdots \oplus a_j = i$$$. Initially, $$$b$$$ is all $$$0$$$. We loop $$$j$$$ from $$$1$$$ to $$$n$$$ and check for each $$$k$$$ if $$$b_k=1$$$. If it is, then there is some position $$$p < j$$$ such that $$$a_1 \oplus a_2 \oplus \cdots \oplus a_p = k$$$. If we take xor of range from $$$(p,j]$$$, then it will be $$$k \oplus a_1 \oplus a_2 \oplus \cdots \oplus a_j$$$ (as $$$a_1 \oplus a_2 \oplus \cdots \oplus a_p$$$ gets cancelled). This $$$a_1 \oplus a_2 \oplus \cdots \oplus a_j$$$ can be stored as we loop ahead. We are looping all possible prefix xors and not all prefix positions because $$$n$$$ is large.
Time Complexity — $$$O(n \cdot 2^8)$$$.