You are given an array $$$a_1, a_2, \ldots, a_n$$$. Find the number of tuples ($$$x, y, z$$$) such that:

We define $$$f(l, r) = a_l \oplus a_{l + 1} \oplus \ldots \oplus a_{r}$$$, where $$$\oplus$$$ denotes the bitwise XOR operation.

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.

Note

In the first case, there are 4 such tuples in the array $$$[6, 2, 4]$$$:

($$$1$$$, $$$2$$$, $$$2$$$): $$$(a_1 \oplus a_2) \oplus (a_2) = 4 \oplus 2 \gt (a_1 \oplus a_2) = 4$$$
($$$1$$$, $$$1$$$, $$$3$$$): $$$(a_1) \oplus (a_1 \oplus a_2 \oplus a_3) = 6 \oplus 0 \gt (a_1 \oplus a_2 \oplus a_3) = 0$$$
($$$1$$$, $$$2$$$, $$$3$$$): $$$(a_1 \oplus a_2) \oplus (a_2 \oplus a_3) = 4 \oplus 6 \gt (a_1 \oplus a_2 \oplus a_3) = 0$$$
($$$1$$$, $$$3$$$, $$$3$$$): $$$(a_1 \oplus a_2 \oplus a_3) \oplus (a_3) = 0 \oplus 4 \gt (a_1 \oplus a_2 \oplus a_3) = 0$$$

In the second test case, there are no such tuples.

A BIT of an Inequality