A Latin Square is an -by- array filled with different digits, each digit occurring exactly once in each row and exactly once in each column.
A Latin Square is in reduced form if the top row and leftmost column are sorted in increasing order.
Given an -by- array, determine if it is a Latin Square, and if so, if it is in reduced form.
The first line contains a single positive integer .
Each of the next lines contains digits in base . The digits 0 through 9 will be represented as is, and the uppercase letters A through Z represent the digits 10 through 35. The digits are guaranteed to be valid in base .
If the array is not a Latin Square, print
No on a single line.
If the array is a Latin Square, but not in reduced form, print
Latin on a single line.
If the array is a Latin Square in reduced form, print
Reduced on a single line.
Sample Input 1
3 012 120 201
Sample Output 1
Sample Input 2
4 3210 0123 2301 1032
Sample Output 2
Sample Input 3
11 0123458372A A9287346283 0285475A834 84738299A02 1947584037A 65848430002 038955873A8 947530200A8 93484721084 95539A92828 04553883568
Sample Output 3
Since the original data were weak, an additional test case was added, partials were disabled, and all submissions were rejudged.