You are given an array $$$a_1, a_2, \dots a_n$$$. Count the number of pairs of indices $$$1 \leq i, j \leq n$$$ such that $$$a_i \lt i \lt a_j \lt j$$$.

Input

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$2 \leq n \leq 2 \cdot 10^5$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \leq a_i \leq 10^9$$$) — the elements of the array.

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the number of pairs of indices satisfying the condition in the statement.

Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).

Note

For the first test cases the pairs are $$$(i, j)$$$ = $$$\{(2, 4), (2, 8), (3, 8)\}$$$.

The pair $$$(2, 4)$$$ is true because $$$a_2 = 1$$$, $$$a_4 = 3$$$ and $$$1 \lt 2 \lt 3 \lt 4$$$.
The pair $$$(2, 8)$$$ is true because $$$a_2 = 1$$$, $$$a_8 = 4$$$ and $$$1 \lt 2 \lt 4 \lt 8$$$.
The pair $$$(3, 8)$$$ is true because $$$a_3 = 2$$$, $$$a_8 = 4$$$ and $$$2 \lt 3 \lt 4 \lt 8$$$.

Yet Another Problem About Pairs Satisfying an Inequality

Examples