You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 7.0 seconds
Memory limit: 512.0 MB

# Problem
You are given an array $$$a$$$ consisting of $$$n$$$ elements. You may apply several operations (possibly zero) to it.

During each operation, you choose two indices $$$i$$$ and $$$j$$$ ($$$1 \le i, j \le n$$$; $$$i \ne j$$$), increase $$$a_j$$$ by $$$a_i$$$, and remove the $$$i$$$-th element from the array (so the indices of all elements to the right to it decrease by $$$1$$$, and $$$n$$$ also decreases by $$$1$$$).

Your goal is to make the array $$$a$$$ strictly ascending. That is, the condition $$$a_1 < a_2 < \dots < a_n$$$ should hold (where $$$n$$$ is the resulting size of the array).

Calculate the minimum number of actions required to make the array strictly ascending.

## Input Format
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 Format
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.

## Examples
```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
```
```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:

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

Now solve the problem and return the code.