CF1342F.Make It Ascending

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 $a_1 \lt a_2 \lt \dots \lt a_n$ should hold (where $n$ is the resulting size of the array).

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

给你一个包含 $n$ 个元素的数组 $a$。你可以对其执行若干次（可能为零次）操作。

每次操作中，你选择两个下标 $i$ 和 $j$（满足 $1 \le i, j \le n$ 且 $i \ne j$），将 $a_j$ 增加 $a_i$，然后从数组中删除第 $i$ 个元素（即其右侧所有元素的下标均减 $1$，同时 $n$ 也减 $1$）。

你的目标是使数组 $a$ 严格递增，即满足 $a_1 \lt a_2 \lt \dots \lt a_n$（其中 $n$ 为操作后数组的最终长度）。

请计算使数组严格递增所需的最少操作次数。

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 $1$.

第一行包含一个整数 $T$（$1 \le T \le 10000$）—— 表示测试用例的数量。

每个测试用例由两行组成。第一行包含一个整数 $n$（$1 \le n \le 15$）—— 表示初始数组 $a$ 中的元素个数。

第二行包含 $n$ 个整数 $a_1$, $a_2$, ..., $a_n$（$1 \le a_i \le 10^6$）。

保证满足以下条件：

• 满足 $n \ge 5$ 的测试用例数量不超过 $5000$；
• 满足 $n \ge 8$ 的测试用例数量不超过 $500$；
• 满足 $n \ge 10$ 的测试用例数量不超过 $100$；
• 满足 $n \ge 11$ 的测试用例数量不超过 $50$；
• 满足 $n \ge 12$ 的测试用例数量不超过 $25$；
• 满足 $n \ge 13$ 的测试用例数量不超过 $10$；
• 满足 $n \ge 14$ 的测试用例数量不超过 $3$；
• 满足 $n \ge 15$ 的测试用例数量不超过 $1$。

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.

对于每个测试用例，按如下格式输出答案：

第一行输出 $k$ —— 你需要执行的最少操作次数。随后输出 $k$ 行，每行包含两个索引 $i$ 和 $j$，表示对应的操作。注意：在从数组中删除元素后，数组中各元素的编号会发生变化。若存在多个最优操作序列，输出其中任意一个即可。

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

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

在第一个测试用例中，操作序列对 $a$ 的修改过程如下：

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