You are given a $N \times M$ matrix of characters. In one operation you can remove a column of the matrix. You can perform as many operations as you want. Your task is to make the final matrix interesting i.e. the string formed by the characters of $i^{th}$ row is lexicographically smaller or equal to the string formed by the characters of the $(i+1)^{th}$ row. You need to use minimum number of operations possible.
An empty matrix is always a interesting matrix.

Input
The first line contains two integers $N$and  $M$.
The next $N$ lines contain $M$ letters each.

Output
In the output, you need to print the minimum number of operations to make the matrix interesting.

Constraints
$1 \le N, M \le 100$

There are only lowercase English alphabets as characters in the input.