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 $n-1$.

### 输入格式

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

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 $25000$ words in the dictionary.

### 输出格式

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

### 样例

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

5 人解决，9 人已尝试。

10 份提交通过，共有 29 份提交。

7.6 EMB 奖励。