Make It Ascending

Description:

Input:

The first line contains one integer $$$T$$$ ($$$1 \le T \le 10000$$$) — the number of test cases.

Each test case consists of two lines. The first line contains one integer $$$n$$$ ($$$1 \le n \le 15$$$) — the number of elements in the initial array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$1 \le a_i \le 10^6$$$).

It is guaranteed that:

• the number of test cases having $$$n \ge 5$$$ is not greater than $$$5000$$$;
• the number of test cases having $$$n \ge 8$$$ is not greater than $$$500$$$;
• the number of test cases having $$$n \ge 10$$$ is not greater than $$$100$$$;
• the number of test cases having $$$n \ge 11$$$ is not greater than $$$50$$$;
• the number of test cases having $$$n \ge 12$$$ is not greater than $$$25$$$;
• the number of test cases having $$$n \ge 13$$$ is not greater than $$$10$$$;
• the number of test cases having $$$n \ge 14$$$ is not greater than $$$3$$$;
• the number of test cases having $$$n \ge 15$$$ is not greater than $$$1$$$.

Output:

For each test case, print the answer as follows:

In the first line, print $$$k$$$ — the minimum number of operations you have to perform. Then print $$$k$$$ lines, each containing two indices $$$i$$$ and $$$j$$$ for the corresponding operation. Note that the numeration of elements in the array changes after removing elements from it. If there are multiple optimal sequences of operations, print any one of them.

Sample Input:

4
8
2 1 3 5 1 2 4 5
15
16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1
2
3 3
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14

Sample Output:

3
6 8
1 6
4 1
7
1 15
1 13
1 11
1 9
1 7
1 5
1 3
1
2 1
0

Note:

In the first test case, the sequence of operations changes $$$a$$$ as follows:

$$$[2, 1, 3, 5, 1, 2, 4, 5] \rightarrow [2, 1, 3, 5, 1, 4, 7] \rightarrow [1, 3, 5, 1, 6, 7] \rightarrow [2, 3, 5, 6, 7]$$$.