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B - Line Sensor

Score : $200$ points

Problem Statement

There is a grid with $H$ rows from top to bottom and $W$ columns from left to right. Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left.
The squares are described by characters $C_{i,j}$. If $C_{i,j}$ is ., $(i, j)$ is empty; if it is #, $(i, j)$ contains a box.

For integers $j$ satisfying $1 \leq j \leq W$, let the integer $X_j$ defined as follows.

• $X_j$ is the number of boxes in the $j$-th column. In other words, $X_j$ is the number of integers $i$ such that $C_{i,j}$ is #.

Find all of $X_1, X_2, \dots, X_W$.

Constraints

• $1 \leq H \leq 1000$
• $1 \leq W \leq 1000$
• $H$ and $W$ are integers.
• $C_{i, j}$ is . or #.

---

Input

The input is given from Standard Input in the following format:

$H$ $W$

$C_{1,1}C_{1,2}\dots C_{1,W}$

$C_{2,1}C_{2,2}\dots C_{2,W}$

$\vdots$

$C_{H,1}C_{H,2}\dots C_{H,W}$

Output

Print $X_1, X_2, \dots, X_W$ in the following format:

``` $X_1$ $X_2$ $\dots$ $X_W$ ```

---

3 4
#..#
.#.#
.#.#

1 2 0 3

In the $1$-st column, one square, $(1, 1)$, contains a box. Thus, $X_1 = 1$.
In the $2$-nd column, two squares, $(2, 2)$ and $(3, 2)$, contain a box. Thus, $X_2 = 2$.
In the $3$-rd column, no squares contain a box. Thus, $X_3 = 0$.
In the $4$-th column, three squares, $(1, 4)$, $(2, 4)$, and $(3, 4)$, contain a box. Thus, $X_4 = 3$.
Therefore, the answer is $(X_1, X_2, X_3, X_4) = (1, 2, 0, 3)$.

---

3 7
.......
.......
.......

0 0 0 0 0 0 0

There may be no square that contains a box.

---

8 3
.#.
###
.#.
.#.
.##
..#
##.
.##

2 7 4

---

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

0 5 1 2 2 0 0 5 3 3 3 3 0 0 1 1 3 1 1 0 0 5 3 3 3 3 0 0 5 1 1 1 5 0 0 3 2 2 2 2 0 0 5 3 3 3 3