D. Manhattan Circle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Given a $$$n$$$ by $$$m$$$ grid consisting of '.' and '#' characters, there exists a whole manhattan circle on the grid. The top left corner of the grid has coordinates $$$(1,1)$$$, and the bottom right corner has coordinates $$$(n, m)$$$.

Point ($$$a, b$$$) belongs to the manhattan circle centered at ($$$h, k$$$) if $$$|h - a| + |k - b| < r$$$, where $$$r$$$ is a positive constant.

On the grid, the set of points that are part of the manhattan circle is marked as '#'. Find the coordinates of the center of the circle.

Input

The first line contains $$$t$$$ ($$$1 \leq t \leq 1000$$$)  — the number of test cases.

The first line of each test case contains $$$n$$$ and $$$m$$$ ($$$1 \leq n \cdot m \leq 2 \cdot 10^5$$$) — the height and width of the grid, respectively.

The next $$$n$$$ lines contains $$$m$$$ characters '.' or '#'. If the character is '#', then the point is part of the manhattan circle.

It is guaranteed the sum of $$$n \cdot m$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$, and there is a whole manhattan circle on the grid.

Output

For each test case, output the two integers, the coordinates of the center of the circle.

Example
Input
6
5 5
.....
.....
..#..
.....
.....
5 5
..#..
.###.
#####
.###.
..#..
5 6
......
......
.#....
###...
.#....
1 1
#
5 6
...#..
..###.
.#####
..###.
...#..
2 10
..........
...#......
Output
3 3
3 3
4 2
1 1
3 4
2 4