gandhi-tree-march

Gandhijee is interested in building human tree. He defined a human node as follows :
Person_Id = English alphabet {a...z} .          
Person_Chain_Definition = Person_Id ( Person_Chain_Definition   Person_Chain_Definition )

For example : 
a( b(..) c( d( . e(..) ) f( . . ) ) ) refers to a human tree having a as the root human, 
whose chain links are are b and c, (spaces here are for clarity, input file has no spaces).   

Note : After every Person_Id there is necessarily an opening parenthesis ( that starts the definition of the sub-tree under the person. For empty(NULL) human nodes, there is a '.' character. 
Now, Gandhijee figure out the tree as follows : 
Step 1 : He writes root human root id in column 0. 
Step 2 : Then he writes left link's person id in 1 column to the left and right link's person id to 1 column to the right. 
He continues writing the subtree, in a way that, for an id written in column C, it's left link's id is written in column C-1 and the right link's id is written in column C+1.   

Now, Gandhijee wants to know the id's of people standing in a particular column C in lexicographically sorted order.
You are provided with column number C and the Tree definition string S. Gandhijee is very busy and hence he wants you to help him.   

Input : 
First line contains a number T, the number of test cases. 
Each test case consists of a single line containing C, the column number for which you need to print the result, followed by a space followed by definition of the tree in the format given above, without any spaces.

Output : 
For each test case, on a new line print the required id's in lexicographically sorted order, without spaces.  
If there are no id's in column C, print "Common Gandhijee!" (quotes for clarity).   

Constraints : 
1 ≤ T ≤ 100  
1 ≤ Len(S) ≤ 10000 
-10000 ≤ C ≤ 10000

Image for given testcase.      SAMPLE INPUT
2
-1 a(c(f(.h(..))b(g(..).))e(.d(..)))
3 b(c(..)a(..))

SAMPLE OUTPUT
cgh
Common Gandhijee!

Explanation

For the 1st sample case, from the diagram clearly c, g, h lies in column -1.

Source: hackerearth | Difficulty: HARD
Tags: Tree algorithms


Solutions: