You are given an array \(A\) of size \(N\). Your task is to find the number of subarrays within the given array such that:

The Bitwise AND of all elements in the subarray has an odd number of set bits (i.e., 1s), and
The Bitwise XOR of all elements in the subarray has an even number of set bits (i.e., 1s)

Note: The subarray of \(A\) is a contiguous part of the array \(A\), i. e. the array \(A_i, A_{i + 1}, ...., A_j\) for some \(1 \leq i \leq j \leq N\).

Input format

The first line contains a single integer \(T\), which denotes the number of test cases.
For each test case:
- The first line contains \(N\) denoting the size of array \(A\).
- The second line contains \(N\) space-separated integers, denoting the elements of \(A\).

Output format

For each test case, print the number of subarrays within the given array such that the Bitwise AND of all elements in the subarray has an odd number of set bits (i.e., 1s) and Bitwise XOR of all elements in the subarray has an even number of set bits (i.e., 1s) in a new line.

Constraints

\(1 \leq T \leq 10^5 \\ 1 \leq N \leq 10^6 \\ 1≤A[i]≤10^9\ ∀\ i∈[1,N] \\ \text{The sum of all values of N over all test cases doesn't exceed } 10^6\)