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.

Solution