You are given a rectangular matrix representing a picture made by Peter. The '#' character represents a black pixel and the '.' character a white pixel. You should count how many stones are on the picture with the respective letters A, B, and C.
The first line contains two integers $W$ and $H$. The next $H$ lines each contain a string of length $W$. The strings are composed of '.' and '#'.
*Limits*
The output should consist of a single line, whose content is three integers $A$, $B$, and $C$ separated with single spaces, indicating the number of stones with the respective marks A, B, and C.
*Sample Explanation*
There are black pixels forming a letter C. These pixels, however, belong to the region around the stones and do not form a mark since they are not surrounded by white pixels.
## Input
The first line contains two integers $W$ and $H$. The next $H$ lines each contain a string of length $W$. The strings are composed of '.' and '#'.*Limits* $7 <= W <= 1000$; $9 <= H <= 1000$.
## Output
The output should consist of a single line, whose content is three integers $A$, $B$, and $C$ separated with single spaces, indicating the number of stones with the respective marks A, B, and C.
[samples]
## Note
*Sample Explanation*There are black pixels forming a letter C. These pixels, however, belong to the region around the stones and do not form a mark since they are not surrounded by white pixels.
**Definitions**
Let $ W, H \in \mathbb{Z}^+ $ denote the width and height of the matrix.
Let $ M \in \{ \text{`.`}, \text{`#`} \}^{H \times W} $ be the binary matrix representing the picture, where `#` denotes a black pixel and `.` denotes a white pixel.
Let $ R \subseteq \{ (i,j) \mid 1 \le i \le H, 1 \le j \le W \} $ be the set of all connected components of black pixels under 4-directional connectivity (up, down, left, right).
For each connected component $ c \in R $, define its **bounding box** as the minimal axis-aligned rectangle enclosing all pixels in $ c $.
Define a **stone** as a connected component $ c \in R $ such that:
- All pixels in $ c $ are part of a **closed contour** forming one of the letters A, B, or C.
- The contour is **fully surrounded by white pixels** (i.e., no black pixel touches the matrix boundary).
- The shape of $ c $ matches the topological structure of one of the letters A, B, or C (as defined by standard pixel-based glyph recognition: A has a triangular top and a horizontal bar; B has two half-circles and a vertical bar; C is a concave curve open to the right).
**Constraints**
1. $ 1 \le W, H \le 100 $
2. Each connected component $ c \in R $ consists of at least 3 pixels.
3. Only components fully enclosed by white pixels (i.e., no pixel in $ c $ is on the matrix boundary) are considered valid stones.
**Objective**
Count the number of valid stone components matching the shapes of letters A, B, and C:
Let $ A = |\{ c \in R \mid c \text{ matches shape A} \}| $,
$ B = |\{ c \in R \mid c \text{ matches shape B} \}| $,
$ C = |\{ c \in R \mid c \text{ matches shape C} \}| $.
Output: $ A \ B \ C $