Background

NFP means the future. When it comes to finance, Noa’s friends all want to hear him say this.

Problem Description

NFP is a cryptocurrency. The value of one NFP over $s$ days can be represented by an $r$-row, $s$-column character matrix containing only the characters . and #. In column $i$, the # in the $j$-th row from bottom to top means that on day $i$ the value of this NFP is $j$.

The “insecurity” of an NFP is defined as the difference between the maximum value it reaches and the minimum value it reaches over the $s$ days.

....##.
#..#...
.##....
......#

As shown above, the values of this NFP over $7$ days are: $3,2,2,3,4,4,1$. Its “insecurity” is $3$.

Now Noa wants you to help him determine the insecurity of the $n$ NFPs he has.

Input Format

The first line contains three integers $n, r, s$, representing the number of NFPs, the number of rows of the matrix, and the number of columns.

Then follow $n$ matrices of size $r \times s$, describing the values of each NFP over $s$ days.

It is guaranteed that in the value matrix of each NFP, every column contains exactly one character #.

Output Format

Output $n$ lines, each being the insecurity of one NFP.

4 2 2
##
..
..
##
#.
.#
.#
#.

0
0
1
1

1 5 8
.....#.#
...#..#.
..#.#...
.#......
#.......

4

2 3 3
...
##.
..#
.#.
#..
..#

1
2

Hint

For $100\%$ of the testdata, $1 \leq n \leq 20$, $2 \leq r, s \leq 50$.

The full score for this problem is $50$ points.

Translated by ChatGPT 5