Mock CCC '18 Contest 1 J4/S2 - A Square Problem

View as PDF

Submit solution


Points: 5 (partial)
Time limit: 5.0s
Memory limit: 1G

Problem type

A Latin Square is an N-by-N array filled with N 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 N-by-N array, determine if it is a Latin Square, and if so, if it is in reduced form.

Constraints

2 \le N \le 36

Input Specification

The first line contains a single positive integer N.

Each of the next N lines contains N digits in base N. 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 N.

Output Specification

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

3
012
120
201

Sample Output

Reduced

Sample Input

4
3210
0123
2301
1032

Sample Output

Latin

Sample Input

11
0123458372A
A9287346283
0285475A834
84738299A02
1947584037A
65848430002
038955873A8
947530200A8
93484721084
95539A92828
04553883568

Sample Output

No

Comments

There are no comments at the moment.