P17204 "DLESS-6" XOR and MEX

**The input size of this problem is large. Please use a fast input method.**

Given a sequence $a$ of length $n$, let $f(a,x)$ be $\operatorname{mex}(a_1\oplus x,a_2\oplus x,\ldots,a_n\oplus x)^{\dagger}$. Find $\min_{x=0}^{\infty}(x+f(a,x))$. Here, $\oplus$ denotes the bitwise XOR operation. --- $^\dagger$ For natural numbers $x_1,x_2\ldots,x_n$, $\operatorname{mex}(x_1,x_2,\ldots,x_n)$ denotes the smallest non-negative integer that does not appear among $x_1,x_2,\ldots,x_n$.

**This problem has multiple test cases.** The first line contains a positive integer $T$, representing the number of test cases. For each test case: - The first line contains a positive integer $n$. - The second line contains $n$ numbers, representing the sequence $a$.

For each test case, output one line with one number, representing the answer.

**[Sample Explanation]** For the first test case, take $x=0$, then $f(a,0)=\operatorname{mex}(1,4,5,2,6)=0$. Obviously, there cannot be an answer smaller than $0$. For the second test case, take $x=1$, then $f(a,1)=\operatorname{mex}(1,0,5,4,3,7)=2$. It can be proven that $3$ is the minimum value of $x+f(a,x)$. **[Constraints]** For all testdata, it is guaranteed that: - $1\le T\le 20$; - $1\le n\le 10^6$; - $\forall i\in[1,n],0\le a_i