CF496C.Removing Columns

You are given an n × m rectangular table consisting of lower case English letters. In one operation you can completely remove one column from the table. The remaining parts are combined forming a new table. For example, after removing the second column from the table

abcd
edfg
hijk

we obtain the table:

acd
efg
hjk

A table is called good if its rows are ordered from top to bottom lexicographically, i.e. each row is lexicographically no larger than the following one. Determine the minimum number of operations of removing a column needed to make a given table good.

给你一个由小写英文字母组成的 $n \times m$ 矩形表格。一次操作可以完全删除表格中的一列，剩余部分将合并形成一张新表格。例如，从下表中删除第二列后：

abcd
edfg
hijk

得到的新表为：

acd
efg
hjk

若一张表的各行从上到下按字典序非递减排列（即每一行的字典序均不大于其下一行），则称该表为“好表”。请确定使给定表格变为“好表”所需的最少列删除操作次数。

The first line contains two integers — n and m (1 ≤ n, m ≤ 100).

Next n lines contain m small English letters each — the characters of the table.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 100$）。

接下来的 $n$ 行，每行包含 $m$ 个小写英文字母——即表格中的字符。

Print a single number — the minimum number of columns that you need to remove in order to make the table good.

输出一个整数——为使表格变为“好表格”所需删除的最少列数。

In the first sample the table is already good.

In the second sample you may remove the first and third column.

In the third sample you have to remove all the columns (note that the table where all rows are empty is considered good by definition).

Let strings s and t have equal length. Then, s is lexicographically larger than t if they are not equal and the character following the largest common prefix of s and t (the prefix may be empty) in s is alphabetically larger than the corresponding character of t.

在第一个样例中，表格已经满足要求。

在第二个样例中，你可以移除第一列和第三列。

在第三个样例中，你必须移除所有列（注意：根据定义，所有行均为空的表格被视为满足要求）。

设字符串 $s$ 与 $t$ 长度相等。若 $s \ne t$，且在 $s$ 与 $t$ 的最长公共前缀（该前缀可以为空）之后，$s$ 中紧接着的字符在字母表中的顺序大于 $t$ 中对应位置的字符，则称 $s$ 字典序大于 $t$。