Strong Pairs

Time Limit	Memory	Input	Output
1 s	64 MB	stdin	stdout

A workshop has $n$ sensors lying on a table, and the $i$ -th of them has an id $a_{i}$ . Two sensors can be linked together only if they are strong together, which the manual defines like this: sensors $i$ and $j$ form a strong pair when

a_{i} & a_{j} \geq a_{i} \oplus a_{j}

where $&$ denotes the bitwise AND operation and $\oplus$ denotes the bitwise XOR operation.

Count how many strong pairs $(i, j)$ with $i < j$ there are. Two sensors lying at different places on the table are always a different pair, even when they happen to carry the same id.

Input

First line of input will be a single integer $t$ - the number of testcases.
Each testcase takes two lines. The first line has a single integer $n$ - the number of sensors. The second line has $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ - their ids.

Output

For every testcase print a single line with the number of strong pairs.

Example

Input

Output

1
2
0

In the first testcase the only strong pair is $(4, 7)$ , because $4 & 7 = 4$ while $4 \oplus 7 = 3$ . In the third testcase $2 & 4 = 0$ and $2 \oplus 4 = 6$ , so that pair is not strong and the answer is $0$ .

Constraints

$1 \leq t \leq 10$
$1 \leq n \leq 1 0^{5}$
$1 \leq a_{i} \leq 1 0^{9}$
The sum of $n$ over all testcases does not exceed $1 0^{5}$ .

This problem was adapted from Rock and Lever, problem B of Codeforces Round 672 (Div. 2).

Input

Output

Example

Constraints

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