Make It Ascending

题意翻译

给予一个包含$n$个元素的数组$a$，你可以进行以下操作： - 选择两个不同的元素$a_i,a_j$（$1 \le i,j \le n$，$i \ne j$） - 将$a_j$的值加上$a_i$，并移除$a$中的第$i$个元素。 求使$a$数组严格递增（对于$1 \le i < n$，有$a_i<a_{i+1}$）所需的最少操作数（可以为$0$）。 输入有多组数据（$1 \le T \le 10000$），且保证： - $1 \le a_i\le 10^6$ - $1 \le n \le 15$ - 在单个测试点中,满足以下条件的数据与出现次数$t$ 的关系满足： | $n \ge$ | $t \le$ | | -----------: | -----------: | | $5$| $5000$| | $8$| $500$| | $10$| $100$| | $11$| $50$| | $12$| $25$| | $13$| $10$| | $14$| $3$| | $15$| $1$| 例如：$n=15$的数据在一个测试点中至多出现一次。

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

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

说明

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] $ .