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B. Forming Triangles

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou have $$$n$$$ sticks, numbered from $$$1$$$ to $$$n$$$. The length of the $$$i$$$-th stick is $$$2^{a_i}$$$.

You want to choose exactly $$$3$$$ sticks out of the given $$$n$$$ sticks, and form a non-degenerate triangle out of them, using the sticks as the sides of the triangle. A triangle is called non-degenerate if its area is strictly greater than $$$0$$$.

You have to calculate the number of ways to choose exactly $$$3$$$ sticks so that a triangle can be formed out of them. Note that the order of choosing sticks does not matter (for example, choosing the $$$1$$$-st, $$$2$$$-nd and $$$4$$$-th stick is the same as choosing the $$$2$$$-nd, $$$4$$$-th and $$$1$$$-st stick).

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of two lines:

- the first line contains one integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$);
- the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le n$$$).

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

For each test case, print one integer — the number of ways to choose exactly $$$3$$$ sticks so that a triangle can be formed out of them.

Example

Input

471 1 1 1 1 1 143 2 1 331 2 311

Output

35 2 0 0

Note

In the first test case of the example, any three sticks out of the given $$$7$$$ can be chosen.

In the second test case of the example, you can choose the $$$1$$$-st, $$$2$$$-nd and $$$4$$$-th stick, or the $$$1$$$-st, $$$3$$$-rd and $$$4$$$-th stick.

In the third test case of the example, you cannot form a triangle out of the given sticks with lengths $$$2$$$, $$$4$$$ and $$$8$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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