When a geometric problem is extended to three dimensions or even higher dimensions, its difficulty can increase significantly. To address complex $$$n$$$-dimensional geometric structures, researchers have proposed a model in which the $$$2^n$$$ key positions in space are abstracted as vertices of a graph, and specific geometric constraints between these positions are abstracted as edges in the graph.

You now have a model that has been abstracted into a graph, in which complex geometric features have been transformed into a simple undirected graph containing $$$2^n$$$ vertices with no duplicate edges or self-loops. However, for certain reasons, you cannot directly observe the edges in the graph. You want to know the total number of edges, $$$m$$$.

You may use a "subset detection detector" which works as follows:

• You input a subset $$$S$$$ containing $$$k$$$ vertices into the detector. The detector requires that the size of each set examined must be exactly half the total number of vertices in the graph, i.e., $$$k = 2^{n-1}$$$.
• The detector scans these vertices and their associated edges, and returns the total number of edges in the graph where at least one endpoint belongs to the set $$$S$$$.

Due to the high cost, the detector can be used at most $$$2^{n+1}$$$ times. Given the limited number of queries, find the total number of edges $$$m$$$ in the graph.

First, read an integer $$$n$$$ from standard input ($$$1 \le n \le 10$$$). This means the graph contains $$$2^n$$$ vertices, numbered from $$$1$$$ to $$$2^n$$$.

To make a query, output ? s to standard output, where $$$s$$$ is a binary string of length $$$2^n$$$. The $$$i$$$-th character should be:

• 1, if vertex $$$i$$$ is included in $$$S$$$;
• 0, otherwise.

You must ensure that the number of 1s in the string is exactly $$$2^{n-1}$$$. If you make an invalid query or exceed the query limit, the interactor will terminate your program.

After each query, you need to read an integer $$$d$$$ from standard input, which denotes the number of edges that have at least one endpoint in the subset $$$S$$$.

To output the answer, output ! m to standard output, where $$$m$$$ is the total number of edges. After outputting the answer, you must terminate the program immediately.

The interactor is non-adaptive. This means that the graph is fixed before the interaction begins and does not change according to your queries.

Note: After each output, you must print a newline and flush the standard output buffer. Use the following methods to flush:

• For C or C++, use fflush(stdout) or cout.flush()
• For Java, use System.out.flush()
• For Python, use stdout.flush()