This is an interactive problem.

There is an undirected simple graph with $100$ vertices.

In each query, you can ask the interactor about three vertices $a, b, c$. The interactor will tell you how many edges exist between these three vertices and return an integer in $\{0, 1, 2, 3\}$. You must ensure that $a, b, c$ are pairwise distinct.

You need to reconstruct this graph.

Implementation Details

This problem uses IO interaction. You need to submit a source file that can be compiled, just like a traditional problem.

You do not need to read any input initially. You can initiate a query by writing ? a b c to standard output, and then read an integer between $0$ and $3$ from standard input, which represents the interactor's response.

When you are able to reconstruct the graph, output a line containing ! followed by $100$ lines, each containing a $0/1$ string $s_i$ of length $100$, describing the graph. $s_{i,j}$ is $1$ if and only if the edge $(i, j)$ exists in the graph.

Remember to flush the output after each operation.

Examples

Input 1

0
2
2

Output 1

? 1 2 3
? 1 2 4
? 1 3 4
!
0001
0001
0001
1110

Note

For convenience, we assume there are only $4$ vertices in the graph in this example. Note that in the actual tests, the graph will have $100$ vertices.

Constraints

All test cases have exactly $100$ vertices.

Let $Q$ be the number of your queries. If $Q > 161\,700$, or your returned answer is incorrect, or you perform an illegal interaction process, you will receive $0$ points.

Otherwise, your score will be calculated according to the table below: