### Problem Statement

A word A is called an anagram of a word B if it is possible to change the order of letters in A to get the word B. For example, "coder" is an anagram of "decor".

A word A is called a subword of a word B if A can be obtained from B by removing some letters (possibly 0) from the beginning of B, and removing some letters (possibly 0) from the end of B. For example, "coder" is a subword of "decoder".

A word A is called a subanagram of a word B if there is a word C such that C is an anagram of B and A is a subword of C. For example, "coder" is a subanagram of "record" because the word "coderr" is an anagram of "record" and contains "coder" as a subword.

Let words A and B have the same number of characters. We say that word A dominates word B if for all i, the i-th letter of A is equal to the i-th letter of B or comes after it alphabetically. For example, the word "coder" dominates the word "amber", but doesn't dominate the word "after" (because the 3-rd letter of "coder" is "d" which comes alphabetically before "t" - the 3-rd letter of "after").

A sequence of words A0, A1, ..., An-1 of equal length is called a chain if, for all i from 1 to n-1, word Ai dominates word Ai-1.

You are given a String[] B. Return the maximal value of k where there exists a chain A0, A1, ..., An-1 such that all words in the chain have length k, and for all i, word Ai is a subanagram of word B[i].

### Definition

 Class: LongestSubanagramChain Method: getLength Parameters: String[] Returns: int Method signature: int getLength(String[] B) (be sure your method is public)

### Constraints

-B will contain between 1 and 50 elements, inclusive.
-Each element of B will contain between 1 and 50 characters, inclusive.
-Each element of B will contain only lowercase letters ('a'-'z').

### Examples

0)

 `{"abaa", "abab", "aaba", "babb"}`
`Returns: 3`
 In this example the required chain is, for example, "aaa", "aba", "aba", "bbb".
1)

 `{"aa", "bbb", "ccc", "ddd", "eee"}`
`Returns: 2`
 Note that elements of B can have different length.
2)

 `{"coder", "coding", "topcoder", "program"}`
`Returns: 4`
3)

 `{"b", "a"}`
`Returns: 0`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7501

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10898&pm=7501

andrewzta

#### Testers:

PabloGilberto , radeye , Cosmin.ro , Olexiy , ivan_metelsky

#### Problem categories:

Greedy, Search, Sorting