Every sequence of small letters a and b (also the empty sequence) is called an ab-word. If X=[x₁,..,x_n] is an ab-word and i,j are integers such that 1<=i<=j<=n then X[i..j] denotes the subword of X consisting of the letters x_i,..,x_j. We say that an ab-word X=[x₁,..x_n] is nice if it has as many letters a as b and for all i=1,...,n the subword X[1,i] has at least as many letters a as b.

Now, we give the inductive definition of the similarity between nice ab-words.

• Every two empty ab-words (i.e. words with no letters) are similar
• Two non-empty nice ab-words X=[x₁,...,x_n] and Y=[y₁,..,y_m] are similar if they have the same length (n=m) and one of the following conditions if fulfilled:
  1. x1=y1, xn=yn and X[2..n-1] and Y[2..n-1] are similar ab-words and they are both nice;
  2. there exists i, 1<=i<=n, such that X[1..i], X[i+1..n] are nice ab-words and
  1. Y[1..i], Y[i+1..n] are nice ab-words and X[1..i] is similar to Y[1..i] and X[i+1..n] is similar to Y[i+1..n], or
  2. Y[1..n-i], Y[n-i+1..n] are nice ab-words and X[1..i] is similar to Y[n-i+1..n] and X[i+1..n] is similar to Y[1..n-i].

A level of diversity of a non-empty set S of nice ab-words is the maximal number of ab-words that can be chosen from S in such a way that for each pair w₁,w₂ of chosen words, w₁ is not similar to w₂.

Task

Write a program that:

• reads elements of S from the text file ABS.IN;
• computes the level of diversity of the set S
• writes the result in the text file ABS.OUT.

Input

In the first line of the input file there is a number n of elements of the set S, 1<=n<=1000; in the following n lines there are elements of the set S, i.e. nice ab-words (one word in each line); the first letter of every ab-word is the first symbol in line and there are no spaces between two consecutive letters in the word; the length of every ab-word is an integer from the range [1..200].

Output

In the first and only line of the text file ABS.OUT there should be written one integer - the level of diversity of S.

Example

For the input file ABS.IN:

3
aabaabbbab
abababaabb
abaaabbabb

The correct answer is the output file ABS.OUT

2