Given an array $A$ of size $N$, you could choose some non-negative number $X$ and change every element of the given array to $A_i = A_i \oplus X$

Here, $\oplus$ denotes the bitwise XOR operation.

Print the number of total possible values of $X$ for which bitwise OR of every element of the array would be minimum.

Input format

• The first line contains $T$ denoting the number of test cases.
• The first line of each test case contains integers $N$, denoting the size of the array $A$.
• The next line contains $N$ integers.

Output format

Print the number of total possible values of $X$ for which bitwise OR of every element of the array would be minimum.

Constraints

$1 \leq T \leq 5000$
$1 \leq N \leq 10^5$
$0 \leq A_i \leq 10^9$

The sum of $N$ over all test cases does not exceed $2 \cdot 10^5$