XOR and AND ~ Multiplex Coder

Alice has an array

A

of length

N

. She is interested in finding the number of pairs

(i, j)

such that

1 \leq i < j \leq N

and

A_{i} \oplus A_{j} < A_{i} & A_{j}

$\oplus$

represents the Bitwise XOR operator.

&

represents the Bitwise AND operator.

— number of test cases. Then the test cases follow.

Each test case contains two lines of input.

The first line of each test case contains an integer

N

, the length of the array

A

The second line of each test case contains

N

space-separated integers

A_{1}, A_{2}, \dots, A_{N}

For each test case, output the number of pairs $(i, j)$

such that

1 \leq i < j \leq N

and

A_{i} \oplus A_{j} < A_{i} & A_{j}

1 \leq N \leq 10^{5}

1 \leq A_{i} \leq 10^{9}

Sum of

N

over all test cases does not exceed

3 \cdot 10^{5}

2
1

Test case $1$

: The two pairs of indices satisfying the condition are

(1, 2)

and

(3, 4)

, because

and

A_{1} & A_{2} = 1

A_{3} \oplus A_{4} = 1

and

A_{3} & A_{4} = 2

Test case $2$

: The only pair of indices satisfying the condition is

(2, 3)