This is an interactive problem.

There is an $$$n$$$ by $$$n$$$ grid of conveyor belts, in positions $$$(1, 1)$$$ through $$$(n, n)$$$ of a coordinate plane. Every other square in the plane is empty. Each conveyor belt can be configured to move boxes up ('^'), down ('v'), left ('<'), or right ('>'). If a box moves onto an empty square, it stops moving.

However, one of the $$$n^2$$$ belts is stuck, and will always move boxes in the same direction, no matter how it is configured. Your goal is to perform a series of tests to determine which conveyor belt is stuck, and the direction in which it sends items.

To achieve this, you can perform up to $$$25$$$ tests. In each test, you assign a direction to all $$$n^2$$$ belts, place a box on top of one of them, and then turn all of the conveyors on.

One possible result of a query with $$$n=4$$$. In this case, the box starts at $$$(2, 2)$$$. If there were no stuck conveyor, it would end up at $$$(5, 4)$$$, but because of the stuck '>' conveyor at $$$(3, 3)$$$, it enters an infinite loop.

The conveyors move the box around too quickly for you to see, so the only information you receive from a test is whether the box eventually stopped moving, and if so, the coordinates of its final position.

You begin the interaction by reading a single integer $$$n$$$ ($$$2 \le n\le 100$$$) — the number of rows and columns in the grid.

Then, you can make at most $$$25$$$ queries.

Each query should begin with a line of the form ? r c, where r and c are the initial row and column of the box, respectively.

The next $$$n$$$ lines of the query should contain $$$n$$$ characters each. The $$$j$$$th character of the $$$i$$$th row should be one of '^', 'v', '<', or '>', indicating the direction of conveyor $$$(i, j)$$$ for this query.

After each query, you will receive two integers $$$x$$$ and $$$y$$$. If $$$x = y = -1$$$, then the box entered an infinite loop. Otherwise, its final position was $$$(x, y)$$$.

If you make too many queries or make an invalid query, you will receive the Wrong Answer verdict.

After you have found the stuck conveyor and its direction, print a single line ! r c dir, where r and c are the row and column of the stuck conveyor, respectively, and dir is one of '^', 'v', '<', or '>', indicating the direction of the stuck conveyor. Note that printing this answer does not count towards your total of $$$25$$$ queries. After printing this line, your program should terminate.

The interactor is non-adaptive. This means that the location and direction of the stuck belt is fixed at the start of the interaction, and does not change after the queries.

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

• fflush(stdout) or cout.flush() in C++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see the documentation for other languages.

Hacks

To make a hack, use the following format.

The first line should contain a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of rows and columns in the grid.

The next line should contain two integers $$$r$$$ and $$$c$$$ ($$$1 \le r, c \le n$$$), as well as a character $$$\mathrm{dir}$$$ ($$$\mathrm{dir}$$$ is one of '^', 'v', '<', '>') — the position of the stuck conveyor and its fixed direction. These values should be separated by spaces.