Edit Step Ladders

An edit step is a transformation from one word $x$ to another word $y$ such that $x$ and $y$ are words in the dictionary, and $x$ can be transformed to $y$ by adding, deleting, or changing one letter. So the transformation from “dig” to “dog” or from “dog” to “do” are both edit steps. An edit step ladder is a lexicographically ordered sequence of words $w_1, w_2, \ldots w_ n$ such that the transformation from $w_ i$ to $w_{i+1}$ is an edit step for all $i$ from $1$ to $n-1$.

For a given dictionary, you are to compute the length of the longest edit step ladder.

Input

The input to your program consists of the dictionary – a set of lower case words in lexicographic order – one per line. No word exceeds $16$ letters and there are no more than $50\, 000$ words in the dictionary.

Output

The output consists of a single integer, the number of words in the longest edit step ladder.

Sample Input 1 Sample Output 1
cat
dig
dog
fig
fin
fine
fog
log
wine
5