[Solution] Max Shift After XOR CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Max Shift After XOR CodeChef Solution | CodeChef Problem Solution 2022

You are given an array A$A$, consisting of N$N$ integers.

Consider the following definitions:

• Prefix xor array of an array A$A$ is defined as the array B$B$ such that Bi=A1⊕…⊕Ai$B_i=A_1\oplus \dots \oplus A_i$, where ⊕$\oplus$ denotes bitwise XOR operation.
  In other words, B=[A1,A1⊕A2,…,A1⊕A2…⊕AN]$B=[A_1,A_1\oplus A_2,\dots ,A_1\oplus A_2\dots \oplus A_N]$
• The value of an array A$A$ is the number of distinct values in array B$B$. For example, for array A=[1,2,3,0]$A=[1,2,3,0]$, we have B=[1,3,0,0]$B=[1,3,0,0]$. The array B$B$ has 3$3$ distinct values, thus, the value of array A$A$ is 3$3$.
• One right shift on the array A$A$ is a transformation that changes the array A=[A1,A2…,AN]$A=[A_1,A_2\dots ,A_N]$ to A′=[AN,A1,…,AN−1]$A^{{}^{\prime }}=[A_N,A_1,\dots ,A_{N-1}]$.

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Calculate the maximum value of the array A$A$ you can get, by performing any (possibly zero) number of right shifts on the array A$A$.

Input Format

• The first line of input contains T$T$ −$-$ the number of test cases you need to solve.
• The first line of each test case contains one integer N$N$ −$-$ the size of the array.
• The second line of each test case contains N$N$ space-separated integers A1,…,AN$A_1,\dots ,A_N$ −$-$ the

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•  elements of the array A$A$.

Output Format

For each test case, output on a new line the maximum value of an array A$A$ you can achieve after performing any (possibly zero) number of right shifts on the array.

Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 2≤N≤2⋅105$2\le N\le 2\cdot {10}^5$
• 0≤Ai≤260−1$0\le A_i\le 2^{60}-1$
• Sum of N$N$ over all test cases doesn't exceed 2⋅105$2\cdot {10}^5$.