Uzbek platform kep.uz hosts competitions of various types. One of them is called "Arena".

Anvar took part in some number of battles, which are given by string $$$s$$$. Each element $$$s[i]$$$ can be either "$$$\rm{W}$$$", "$$$\rm{D}$$$", or "$$$\rm{L}$$$", denoting a Win, Draw, or Loss, respectively.

Anvar receives $$$2$$$ points for a win, $$$1$$$ point for a draw, and $$$0$$$ points for losing. However, if Anvar wins three times in a row, he gets an additional $$$1$$$ point starting from the third win. The bonus continues until Anvar draws or loses.

Anvar can ask the administrator of kep.uz to remove some records (possibly none, or all) of his battles, without changing the order of the rest. Find the maximum number of points Anvar can get.

Let $$$f(x)$$$ be the count of character $$$x$$$ in string $$$s$$$.

This is an interactive problem.

Asadullo had an array $$$p[0], p[1], \ldots, p[n - 1]$$$, where each number from $$$0$$$ to $$$n-1$$$ occurs exactly once in some order.

However, evil Dr. Dilyor has stolen Asadullo's array. Sadly, Asadullo doesn't remember any information about his array. Dr. Dilyor proposed a game where Asadullo can give some queries and Dr. Dilyor will answer them.

Let's say Asadullo chooses some sequence of integers $$$x[0], x[1], \ldots, x[m-1]$$$ of size $$$m$$$ ($$$0 \le x[i] \le n-1$$$). Then, Dr. Dilyor returns the number of indices $$$0 \le i \le m - 2$$$ such that $$$p[x[i]] \gt p[x[i + 1]]$$$. Note that the values of the sequence $$$x$$$ do not have to be distinct. Also, the size $$$m$$$ can be chosen independently for each query.

Dr. Dilyor can answer only $$$10\;000$$$ such queries, and the total size of sequences should not exceed $$$10^6$$$. Help Asadullo to restore his array.

First, you should read an integer $$$n$$$ – the size of the array. ($$$1 \le n \le 128$$$)

To make a query, use the following format:

? m x[0] x[1] ... x[m-1]

Then, you will receive an integer $$$k$$$ – the number of indices $$$0 \le i \le m - 2$$$ such that $$$p[x[i]] \gt p[x[i + 1]]$$$.

Once you found the array, print it in the following format:

! p[0] p[1] ... p[n-1]

After this, you must immediately terminate the program.

After printing a query, do not forget to output the end of the line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

• fflush(stdout), cout.flush(), or cout«endl in C++;
• System.out.flush() in Java;
• stdout.flush() in Python;

If you make more than $$$10\;000$$$ queries, or the sum of values $$$m$$$ exceeds $$$10^6$$$, or you incorrectly guess the array $$$p$$$, you will get verdict Wrong Answer.

Also, you can get partial score in the 2nd subtask. Let $$$q$$$ be the maximum number of queries among all tests in subtask 2. Then, your score will be as follows:

There are $$$n$$$ cities in Dadorlandtiria, and cities are connected with $$$m$$$ undirected roads. The $$$i$$$-th road connects cities $$$u[i]$$$ and $$$v[i]$$$. Cities are numbered from $$$0$$$ to $$$n-1$$$.

Unfortunately, all roads in Dadorlandtiria are too old. That is, after going through the $$$i$$$-th road, the road becomes impassable and needs $$$w[i]$$$ dadorian dollars to be repaired. After crossing, the repaired road becomes impassable again, and it needs another $$$w[i]$$$ dadorian dollars to be passable and so on. Initially, all roads are passable.

Let's say you want to travel from city $$$x$$$ to city $$$y$$$, and then return to city $$$x$$$. Let $$$f(x, y)$$$ be the minimum cost to repair the roads to make the travel possible.

Your task is to count the total number of pairs with $$$f(x, y) \le T$$$, where $$$0 \le x \lt y \le n-1$$$ and $$$T$$$ is a given integer.