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XMLCHECK - XML Checker

XML is an extension of HTML. In XML, the user can introduce a tag set that describes the data that he is working with. There are various rules that determine a valid XML document. The program that you will write will check two of those rules.

Rule I: A beginning tag must have an ending tag. A beginning tag is represented by <tag_name> and the corresponding ending tag is represented by </tag_name>.

Rule II: An element defined by one pair of beginning and ending tags may nest completely inside another pair of beginning and ending tags but they may not overlap.

Valid XML:
<address> <street> 123 Any Street </street> <city> Any City </city> </address>

Invalid XML:
<address> <street> 123 Any Street </street> <city> Any City </address> </city>

Your program will determine if a snippet of XML code conforms to these two rules or not. 

Input

The first line of input will contain a single integer n that indicates the number of data sets to follow. For each data set, the first line will contain a single integer m that indicates the number of lines that follow in that snippet of XML code. 

Output

For each snippet of XML code you will write valid or invalid on a line by itself. 

Example

Input:
2
4
<student>
<name>
John Doe
</student>
2
<gpa>
</gpa>

 

Output:
invalid valid

Added by:BYU Admin
Date:2015-12-15
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 MAWK BC NCSHARP COFFEE DART FORTH GOSU JS-MONKEY JULIA KTLN OCT PROLOG PYPY3 R RACKET SQLITE SWIFT UNLAMBDA
Resource:UIL District 2 2011 #12
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