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

$1\le T\le 5000$
$1\le N\le {10}^5$
$0\le A_i\le {10}^9$

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