You are given an array a consisting of n integers. A subarray (l, r) from array a is defined as non-empty sequence of consecutive elements al, al + 1, ..., ar.
The beauty of a subarray (l, r) is calculated as the _bitwise AND_ for all elements in the subarray:
Your task is to calculate the summation of the beauty of all subarrays (l, r) (1 ≤ l ≤ r ≤ n):
The first line contains an integer T, where T is the number of test cases.
The first line of each test case contains an integer n (1 ≤ n ≤ 105), where n is the size of the array a.
The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106), giving the array a.
For each test case, print a single line containing the summation of the beauty of all subarrays in the given array.
As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use _scanf/printf_ instead of _cin/cout_ in C++, prefer to use _BufferedReader/PrintWriter_ instead of _Scanner/System.out_ in Java.
A _bitwise AND_ takes two equal-length binary representations and performs the logical _AND_ operation on each pair of the corresponding bits, by multiplying them. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). This operation exists in all modern programming languages, for example in language C++ and Java it is marked as *&*.
In the first test case, the answer is calculated as summation of 6 subarrays as follow:
## Input
The first line contains an integer T, where T is the number of test cases.The first line of each test case contains an integer n (1 ≤ n ≤ 105), where n is the size of the array a.The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106), giving the array a.
## Output
For each test case, print a single line containing the summation of the beauty of all subarrays in the given array.
[samples]
## Note
As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use _scanf/printf_ instead of _cin/cout_ in C++, prefer to use _BufferedReader/PrintWriter_ instead of _Scanner/System.out_ in Java.A _bitwise AND_ takes two equal-length binary representations and performs the logical _AND_ operation on each pair of the corresponding bits, by multiplying them. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). This operation exists in all modern programming languages, for example in language C++ and Java it is marked as *&*.In the first test case, the answer is calculated as summation of 6 subarrays as follow: Beauty(1, 1) + Beauty(l, 2) + Beauty(1, 3) + Beauty(2, 2) + Beauty(2, 3) + Beauty(3, 3) (7) + (7 & 11) + (7 & 11 & 9) + (11) + (11 & 9) + (9) = 40
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ n_k \in \mathbb{Z} $ denote the length of the array.
- Let $ A_k = (a_{k,1}, a_{k,2}, \dots, a_{k,n_k}) $ be the array of integers, where $ a_{k,i} \in \mathbb{Z}^+ $.
A subarray $ (l, r) $ is defined for $ 1 \leq l \leq r \leq n_k $, and its beauty is $ \bigwedge_{i=l}^{r} a_{k,i} $, the bitwise AND of all elements in the subarray.
**Constraints**
1. $ 1 \leq T \leq 10^4 $ (implied by constraints on $ n $ and typical CF bounds)
2. For each test case $ k $:
- $ 1 \leq n_k \leq 10^5 $
- $ 1 \leq a_{k,i} \leq 10^6 $ for all $ i \in \{1, \dots, n_k\} $
**Objective**
For each test case $ k $, compute:
$$
S_k = \sum_{l=1}^{n_k} \sum_{r=l}^{n_k} \left( \bigwedge_{i=l}^{r} a_{k,i} \right)
$$
Output $ S_k $ for each test case.