Given a binary array. Find the minimum number of swap operations to be performed such that the Bitwise \(AND\) of any subarray of size > 1 is equal. If it can't be done, print \(-1\). Swap can be defined as interchanging array values at any two indices \(i\) and \(j\).

Input:

The first line contains \(T\), the number of test cases

The first line of each test case contains \(N\), the number of elements in the array

The second line of each test case contains \(N\) integers \((0 \leq a[i] \leq 1)\)

Output:

Print \(T\) lines

Each line should contain the answer for that test case

Constraints :

\(1 \leq T \leq 10^3\)

\(1 \leq N \leq 10^5\)

\(0 \leq a[i] \leq 1\)

The sum of \(N\) over all test cases does not exceed \(10^5\)