A BIT of an Inequality
Description
You are given an array $a_1, a_2, \ldots, a_n$. Find the number of tuples ($x, y, z$) such that:
- $1 \leq x \leq y \leq z \leq n$, and
- $f(x, y) \oplus f(y, z) > f(x, z)$.
We define $f(l, r) = a_l \oplus a_{l + 1} \oplus \ldots \oplus a_{r}$, where $\oplus$ denotes the bitwise XOR operation.
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \leq n \leq 10^5$).
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
For each test case, output a single integer on a new line — the number of described tuples.
Input
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \leq n \leq 10^5$).
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
Output
For each test case, output a single integer on a new line — the number of described tuples.
3
3
6 2 4
1
3
5
7 3 7 2 1
4
0
16
Note
In the first case, there are 4 such tuples in the array $[6, 2, 4]$:
- ($1$, $2$, $2$): $(a_1 \oplus a_2) \oplus (a_2) = 4 \oplus 2 > (a_1 \oplus a_2) = 4$
- ($1$, $1$, $3$): $(a_1) \oplus (a_1 \oplus a_2 \oplus a_3) = 6 \oplus 0 > (a_1 \oplus a_2 \oplus a_3) = 0$
- ($1$, $2$, $3$): $(a_1 \oplus a_2) \oplus (a_2 \oplus a_3) = 4 \oplus 6 > (a_1 \oplus a_2 \oplus a_3) = 0$
- ($1$, $3$, $3$): $(a_1 \oplus a_2 \oplus a_3) \oplus (a_3) = 0 \oplus 4 > (a_1 \oplus a_2 \oplus a_3) = 0$
In the second test case, there are no such tuples.