English · Original
Chinese · Translation
Formal · Original
**This is an interactive problem. In the interaction section below you will see the information about flushing the output.**
In this problem, you will be playing a game with Hongcow. How lucky of you!
Hongcow has a hidden _n_ by _n_ matrix _M_. Let _M__i_, _j_ denote the entry _i_\-th row and _j_\-th column of the matrix. The rows and columns are labeled from 1 to _n_.
The matrix entries are between 0 and 109. In addition, _M__i_, _i_ = 0 for all valid _i_. Your task is to find the minimum value along each row, excluding diagonal elements. Formally, for each _i_, you must find .
To do this, you can ask Hongcow some questions.
A question consists of giving Hongcow a subset of distinct indices {_w_1, _w_2, ..., _w__k_}, with 1 ≤ _k_ ≤ _n_. Hongcow will respond with _n_ integers. The _i_\-th integer will contain the minimum value of _min_1 ≤ _j_ ≤ _k__M__i_, _w__j_.
You may only ask Hongcow at most 20 questions — he thinks you only need that many questions answered.
When you are ready to answer, print out a single integer - 1 on its own line, then _n_ integers on the next line. The _i_\-th integer should be the minimum value in the _i_\-th row of the matrix, excluding the _i_\-th element. Do not forget to flush the final answer as well. Printing the answer does not count as asking a question.
You will get _Wrong Answer_ verdict if
* Your question or answers are not in the format described in this statement.
* You ask strictly more than 20 questions.
* Your question contains duplicate indices.
* The value of _k_ in your question does not lie in the range from 1 to _n_, inclusive.
* Your final answer is not correct.
You will get _Idleness Limit Exceeded_ if you don't print anything or if you forget to flush the output, including for the final answer (more info about flushing output below).
## Input
The first line of input will contain a single integer _n_ (2 ≤ _n_ ≤ 1, 000).
## Output
To print the final answer, print out the string _\-1_ on its own line. Then, the next line should contain _n_ integers. The _i_\-th integer should be the minimum value of the _i_\-th row of the matrix, excluding elements on the diagonal. **Do not forget to flush your answer!**
[samples]
## Interaction
To ask a question, print out a single integer _k_ on its own line, denoting the size of your subset. Then, the next line should contain _k_ integers _w_1, _w_2, ... _w__k_. Note, you must flush your output to get a response.
Hongcow will respond by printing out a line with _n_ integers. The _i_\-th integer in this line represents the minimum value of _M__i_, _w__j_ where _j_ is between 1 and _k_.
You may only ask a question at most 20 times, otherwise, you will get _Wrong Answer_.
To flush you can use (just after printing an integer and end-of-line):
* _fflush(stdout)_ in C++;
* _System.out.flush()_ in Java;
* _stdout.flush()_ in Python;
* _flush(output)_ in Pascal;
* See the documentation for other languages.
**Hacking** To hack someone, use the following format
n
M_{1,1} M_{1,2} ... M_{1,n}
M_{2,1} M_{2,2} ... M_{2,n}
...
M_{n,1} M_{n,2} ... M_{n,n}
Of course, contestant programs will not be able to see this input.
## Note
In the first sample, Hongcow has the hidden matrix
\[
\[0, 3, 2\],
\[5, 0, 7\],
\[4, 8 ,0\],
\]
Here is a more readable version demonstrating the interaction. The column on the left represents Hongcow, while the column on the right represents the contestant.
3
3
1 2 3
0 0 0
1
3
2 7 0
2
1 2
0 0 4
1
2
3 0 8
1
1
0 5 4
-1
2 5 4
For the second sample, it is possible for off-diagonal elements of the matrix to be zero.
*这是一个交互式问题。在下面的交互部分，你将看到有关刷新输出的信息。*
在这个问题中，你将和 Hongcow 玩一个游戏。你真幸运！
Hongcow 有一个隐藏的 #cf_span[n] × #cf_span[n] 矩阵 #cf_span[M]。令 #cf_span[Mi, j] 表示矩阵的第 #cf_span[i] 行、第 #cf_span[j] 列的元素。行和列的编号从 #cf_span[1] 到 #cf_span[n]。
矩阵元素的值在 #cf_span[0] 到 #cf_span[109] 之间。此外，对于所有合法的 #cf_span[i]，都有 #cf_span[Mi, i = 0]。你的任务是找出每一行中除对角线元素外的最小值。形式上，对于每个 #cf_span[i]，你必须找到 。
为了完成这个任务，你可以向 Hongcow 提问。
一个提问由给出一个互不相同的下标集合 #cf_span[{w1, w2, ..., wk}] 组成，其中 #cf_span[1 ≤ k ≤ n]。Hongcow 会返回 #cf_span[n] 个整数。第 #cf_span[i] 个整数表示 #cf_span[min1 ≤ j ≤ kMi, wj] 的值。
你最多只能向 Hongcow 提问 #cf_span[20] 次——他认为你只需要这么多问题的答案。
当你准备好给出答案时，请单独输出一个整数 #cf_span[ - 1]，然后在下一行输出 #cf_span[n] 个整数。第 #cf_span[i] 个整数应为矩阵第 #cf_span[i] 行中除去第 #cf_span[i] 个元素的最小值。同样不要忘记刷新最终答案！输出答案不计入提问次数。
如果你出现以下情况，将获得 _Wrong Answer_：
输入的第一行将包含一个整数 #cf_span[n]（#cf_span[2 ≤ n ≤ 1, 000]）。
要输出最终答案，请单独输出字符串 _-1_，然后下一行输出 #cf_span[n] 个整数。第 #cf_span[i] 个整数应为矩阵第 #cf_span[i] 行中除去对角线元素的最小值。*不要忘记刷新你的答案！*
要提问，请单独输出一个整数 #cf_span[k]，表示你所选子集的大小。然后下一行输出 #cf_span[k] 个整数 #cf_span[w1, w2, ... wk]。注意，你必须刷新输出才能获得响应。
Hongcow 会回复一行包含 #cf_span[n] 个整数。该行中第 #cf_span[i] 个整数表示 #cf_span[Mi, wj] 在 #cf_span[j] 介于 #cf_span[1] 和 #cf_span[k] 时的最小值。
你最多只能提问 #cf_span[20] 次，否则你将获得 _Wrong Answer_。
要刷新输出，可以在输出一个整数并换行后使用：
*Hacking* 要 Hack 他人，请使用以下格式：
当然，参赛程序无法看到此输入。
在第一个样例中，Hongcow 的隐藏矩阵为
下面是一个更易读的交互演示。左侧列代表 Hongcow，右侧列代表参赛者。
对于第二个样例，矩阵的非对角线元素可能为零。
## Input
输入的第一行将包含一个整数 #cf_span[n]（#cf_span[2 ≤ n ≤ 1, 000]）。
## Output
要输出最终答案，请单独输出字符串 _-1_，然后下一行输出 #cf_span[n] 个整数。第 #cf_span[i] 个整数应为矩阵第 #cf_span[i] 行中除去对角线元素的最小值。*不要忘记刷新你的答案！*
[samples]
## Interaction
要提问，请单独输出一个整数 #cf_span[k]，表示你所选子集的大小。然后下一行输出 #cf_span[k] 个整数 #cf_span[w1, w2, ... wk]。注意，你必须刷新输出才能获得响应。Hongcow 会回复一行包含 #cf_span[n] 个整数。该行中第 #cf_span[i] 个整数表示 #cf_span[Mi, wj] 在 #cf_span[j] 介于 #cf_span[1] 和 #cf_span[k] 时的最小值。你最多只能提问 #cf_span[20] 次，否则你将获得 _Wrong Answer_。要刷新输出，可以在输出一个整数并换行后使用：
_fflush(stdout)_ 在 C++ 中；
_System.out.flush()_ 在 Java 中；
_stdout.flush()_ 在 Python 中；
_flush(output)_ 在 Pascal 中；
请参阅其他语言的文档。
*Hacking* 要 Hack 他人，请使用以下格式：
n
M_{1,1} M_{1,2} ... M_{1,n}
M_{2,1} M_{2,2} ... M_{2,n}
...
M_{n,1} M_{n,2} ... M_{n,n}
当然，参赛程序无法看到此输入。
## Note
在第一个样例中，Hongcow 的隐藏矩阵为 [ [0, 3, 2], [5, 0, 7], [4, 8 ,0], ]
下面是一个更易读的交互演示。左侧列代表 Hongcow，右侧列代表参赛者。
3 3 1 2 3
0 0 0 1 3
2 7 0 2 1 2
0 0 4 1 2
3 0 8 1 1
0 5 4 -1 2 5 4
对于第二个样例，矩阵的非对角线元素可能为零。
Let $ n \in \mathbb{N} $, $ 2 \leq n \leq 1000 $.
Let $ M \in \mathbb{Z}^{n \times n} $ be a hidden matrix such that:
- $ M_{i,i} = 0 $ for all $ i \in \{1, 2, \dots, n\} $,
- $ 0 \leq M_{i,j} \leq 10^9 $ for all $ i, j \in \{1, 2, \dots, n\} $, $ i \neq j $.
Define $ r_i = \min_{j \neq i} M_{i,j} $ for each $ i \in \{1, 2, \dots, n\} $.
The goal is to determine the vector $ \mathbf{r} = (r_1, r_2, \dots, r_n) $.
You may query a subset $ S \subseteq \{1, 2, \dots, n\} $ with $ |S| = k $, $ 1 \leq k \leq n $, and receive a response vector $ \mathbf{v} \in \mathbb{Z}^n $, where:
$$
v_i = \min_{j \in S} M_{i,j}, \quad \text{for each } i \in \{1, 2, \dots, n\}.
$$
You are allowed at most 20 queries.
After querying, output $-1$ followed by $ \mathbf{r} $.
API Response (JSON)
{
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"name": "B. Hongcow's Game",
"description": {
"content": "**This is an interactive problem. In the interaction section below you will see the information about flushing the output.** In this problem, you will be playing a game with Hongcow. How lucky of you",
"description_type": "Markdown"
},
"platform": "Codeforces",
"limit": {
"time_limit": 3000,
"memory_limit": 262144
},
"difficulty": "None",
"is_remote": true,
"is_sync": true,
"sync_url": null,
"sign": "CF744B"
},
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"content": "Let $ n \\in \\mathbb{N} $, $ 2 \\leq n \\leq 1000 $. \nLet $ M \\in \\mathbb{Z}^{n \\times n} $ be a hidden matrix such that: \n- $ M_{i,i} = 0 $ for all $ i \\in \\{1, 2, \\dots, n\\} $, \n- $ 0 \\leq M_{i,j} \\...",
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