AB-words
Every sequence of small letters a and b (also the empty sequence) is called an ab-word. If X = [x1, ..., xn] 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 xi, ..., xj. We say that an ab-word X = [x1..xn] 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, ..., xn] and Y = [y1, ..., ym] are similar if they have the same length (n = m) and one of the following conditions if fulfilled:
- x1 = y1, xn = yn and X[2..n-1] and Y[2..n-1] are similar ab-words and they are both nice;
- there exists i, 1 <= i <= n, such that X[1..i], X[i+1..n] are nice ab-words and
- 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
- 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 for each test case:
- reads elements of S from standard input;
- computes the level of diversity of the set S;
- writes the result to standard output.
Input
The number of test cases t is in the first line of input, then t test cases follow separated by an empty line.
In the first line of a test case 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
For each test case your program should output one line with one integer - the level of diversity of S.
Example
Sample input: 1 3 aabaabbbab abababaabb abaaabbabb</p>Sample output: 2