# Latin Square

Given an `n`

by `n`

matrix of letters `matrix`

, return whether there are exactly `n`

different letters that appear in the matrix and each letter appears exactly once in each row and exactly once in each column.

**Constraints**

`1 ≤ n ≤ 250`

where`n`

is the number of rows and columns in`matrix`

https://binarysearch.com/problems/Latin-Square

## Examples

### Example 1

**Input**

- matrix =

```
[['a','b','c'],
['c','a','b'],
['b','c','a']]
```

**Output**

- answer =
`True`

**Explanation**

There are 3 different letters and each letter appears exactly once in each row and column.

### Example 2

**Input**

- matrix =

```
[['a','b','c'],
['d','a','a'],
['b','b','a']]
```

**Output**

- answer =
`False`

**Explanation**

There are 4 different letters, and also “a” and “b” appear twice in the same row.

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