Professor John

Time Limit: 2 Seconds
Memory Limit: 65536 KB

## Sunny Cup 2003 - Preliminary Round

April 20th, 12:00 - 17:00

### Problem H: Professor John

Professor John is investigating a math problem. He has obtained some relations
among several variables. Now he would like to know if there are any other relations
that can be deduced from these obtained ones. Since he has been working for
too long, Professor John decides to grant himself a vacation while assigning
you to do the job. Are you ready?

**Input**

The first line of input contains an integer N, which is the number of test
cases. Then N test cases follow.

For each test case:

the 1st line contains a positive integer m (<= 100) which is the number of
given relations;

the following m lines each contains a given relation, in the format

Variable1<Variable2

or

Variable1>Variable2

A "Variable" is represented by a capital character. There will not
be conflicting relations given.

**Output**

For each test case, first print in one line "Case d:" where d is
the number of the test case, start counting from 1.

Then output all the relations which can be deduced from the given relations
in alphabetical order, in the format Variable1<Variable2. Each relation occupies
one line. No extra space shall be printed. The given relations must NOT be included.

If no new relation is found, output "NONE" in one line.

**Sample Input**

2

3

A<B

C>B

C<D

2

A<B

C<D

**Sample Output**

Case 1:

A<C

A<D

B<D

Case 2:

NONE

Author:

**XU, Chuan**
Source:

**Zhejiang University Local Contest 2003, Preliminary**
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