Two words $W_1$ and $W_2$ are said to be generated from the same word $W$, if the three words have the same length $L$, and you can read both $W_1$ and $W_2$ from $W$ reading exactly $L$ letters starting at a position in $W$. If while reading from $W$ you get to the end of the word you start again from the first position. For example _rdwo_ and _ordw_ are both generated from the same word _word_, the first one is if you start reading from the third position of the word, the second one is if you start from the second position. A word $W$ is generated from the same word $W$ as you can read the word starting at the first position of it.
Given a list of $N$ words, can you find how many different generator words $W$ were used to create the list?
The first line of input contains a single integer $N$ ($1 <= N <= 100$), representing the number of words in the list. The second and last line of input contains $N$ strings separated by a space, representing the $N$ words in the list. Each word in the list will contain only lower case letters from the english alphabet and will have no more than $100$ letters.
Print a single line with an integer, representing the number of different generator words $W$ that were used to create the list.
## Input
The first line of input contains a single integer $N$ ($1 <= N <= 100$), representing the number of words in the list. The second and last line of input contains $N$ strings separated by a space, representing the $N$ words in the list. Each word in the list will contain only lower case letters from the english alphabet and will have no more than $100$ letters.
## Output
Print a single line with an integer, representing the number of different generator words $W$ that were used to create the list.
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**Definitions**
Let $ T \in \mathbb{Z}^+ $ be the number of test cases.
For each test case:
- Let $ n, m \in \mathbb{Z}^+ $ denote the dimensions of the board, with $ 5 \leq n, m \leq 10^3 $.
- Let $ B \subseteq \{1, \dots, n\} \times \{1, \dots, m\} $ be the set of positions occupied by black stones ($ a_{i,j} = 1 $).
- Let $ W \subseteq \{1, \dots, n\} \times \{1, \dots, m\} $ be the set of positions occupied by white stones ($ a_{i,j} = 2 $).
- Let $ E = \{ (i,j) \mid a_{i,j} = 0 \} $ be the set of empty positions.
**Constraints**
1. $ 1 \leq T \leq 100 $
2. $ \sum_{\text{test cases}} n \cdot m \leq 10^6 $
3. $ |B| = |W| $
4. $ |E| \geq 2 $
5. Neither black nor white has five-in-a-row in the current position.
**Objective**
Determine the optimal move for black (to be placed on some $ (x,y) \in E $):
- **Win**: If there exists $ (x,y) \in E $ such that placing a black stone at $ (x,y) $ creates a line (horizontal, vertical, or diagonal) of ≥5 consecutive black stones. Among all such moves, choose the lexicographically smallest $ (x,y) $ (min $ x $, then min $ y $).
- **Defense**: If no winning move exists, but there exists $ (x,y) \in E $ such that placing a black stone at $ (x,y) $ blocks *all* potential white winning moves in the next turn (i.e., for every $ (u,v) \in E \setminus \{(x,y)\} $, placing white at $ (u,v) $ does *not* create a five-in-a-row). Among all such defensive moves, choose the lexicographically smallest $ (x,y) $.
- **Defeated**: If neither a winning nor a defensive move exists.