K. Typographic Kaleidoscope
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

You have an "ASCII Art" image formed by the characters '#' and '.', such as the following:

It is known that the image is actually formed by several copies of the letters T, A, and P that we see in the image above. These letters cannot be stretched or scaled; they must have exactly the same shape as those shown. Each character '#' in the image must belong to exactly one letter, and the letters must cover all the '#', without overlapping or covering a '.'.

For example, the following image:

contains two T's and one P. For illustrative purposes, each individual letter is indicated as A, B, and C below:

Given a valid image, how many T's, how many A's, and how many P's are there?

Input

One line with two integers, $$$N$$$ and $$$M$$$ $$$(1\leq N,M\leq 1000)$$$, the number of rows and columns. The following $$$N$$$ lines make up the image, and each contains a string of $$$M$$$ characters.

The given image will always be valid, meaning it can be formed with the letters T, A, P following the rules explained in the statement.

Output

A single line with three integers indicating the quantities of T, A, and P.

If there is more than one possible triplet of values, any of them will be accepted.

Examples
Input
7 13
.............
.###.###.###.
..#..#.#.#.#.
..#..###.###.
..#..#.#.#...
..#..#.#.#...
.............
Output
1 1 1
Input
9 6
###...
.####.
.##.#.
.####.
.#####
..#.#.
....#.
....#.
....#.
Output
2 0 1
Input
11 7
.###...
..####.
..##.#.
..####.
..#####
####.#.
.#####.
.##.##.
.#####.
.##.#..
..#.#..
Output
3 1 1
Note

In the first example, the image contains exactly one T, one A, and one P.

The second example is explained in the statement.