[Solution] Subarray Removal CodeChef Solution

Problem

Chef has a binary array $A$ of length $N$. In one operation, Chef does the following:

1. Select any $L$ and $R$ such that $(1 \le L \lt R \le |A|)$$\\$2. Add $A_L \oplus A_{L+1} \oplus \ldots \oplus A_R$ to his score (Here, $\oplus$ denotes the bitwise XOR operation)$\\$3. Remove the subarray $A_{L \dots R}$ from $A$

Determine the maximum score Chef can get after performing the above operation any number of times.

Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer $N$ — the size of the array $A$.
• The second line of each test case contains $N$ space-separated integers $A_1, A_2, \dots, A_N$ denoting the array $A$.

Output Format

For each test case, output the maximum score Chef can get.

Explanation:

Test Case 1: We can perform the following moves:

• $A = [1, 0, 0, 0, 1]$. Select $L = 1$ and $R = 3$ and remove subarray $[1, 0, 0]$. $A$ becomes $[0, 1]$.
• $A = [0, 1]$. Select $L = 1$ and $R = 2$ and remove subarray $[0, 1]$. $A$ becomes $[]$.

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Total score $= 1 + 1 = 2$

Test Case 2: We can perform the following move:

• $A = [1, 1, 1]$. Select $L = 1$ and $R = 3$ and remove subarray $[1, 1, 1]$. $A$ becomes $[]$.

Total score $= 1$