NITTROAD  Roads of NITT
The Institute of NITT believes in frugality. So when they made the plan for interconnecting the N hostels, they decided to construct as few bidirectional roads as possible. The hostels are interconnected with roads in such a way that every pair of hostels is connected by exactly one path.
Moreover, they were so frugal that they used low quality tar in making the roads. As a result, the roads start to crack and cannot be used anymore.
Now Alpa has a set of queries. At the time of each query, he knows the roads that are unusable. He wants to find the number of pairs of hostels that are disconnected, i.e, the number of pairs (x,y) such that 1 <= x < y <= N and there exists no path between hostels x and y.
Help him find the result for each query.
Constraints:
Test cases <= 5
No. of hostels, N <= 20000
No. of queries, Q <= 20000
Input
First line contains t, the total test cases.
Each test case looks as follows:
First line contains N, total number of hostels.
Next N  1 lines contain two integers x and y, indicating that there is a road between x and y. (1 <= x < y <= N). The roads are numbered from 1 to N  1.
Next line contains Q, total number of queries.
Next Q lines contain the Q queries.
Each query may be of the following two forms:
R x  Remove the road numbered x. It is guaranteed that this road existsand hasn't already been removed.
Q  Output the total number of pairs (x, y) such that 1 <= x < y <= N and there exists no path between hostels x and y.
Output
For each test case,
Output a line for each query with the required value.
Print a blank line after each test case.
Example
Input:
2
3
1 2
1 3
5
Q
R 1
Q
R 2
Q
4
1 2
1 3
1 4
7
Q
R 1
Q
R 2
Q
R 3
Q
Output:
0
2
3
0
3
5
6
hide comments
amulyagaur:
20171206 10:01:15
250 comes up with such a nice problem! :)) 

amb1151:
20171203 15:00:20
Can anyone give a hint on how to solve this problem?... 

jayantisswani:
20170930 14:35:40
Do all the vertices become disconnected after executing all the queries ? 

babur:
20170628 05:49:59
Think Reverse....a must do problem 

Vipul Srivastava:
20161214 16:14:14
Couldn't think of the approach myself. A great question to learn new things. If you can't think of the solution by yourself do take help don't leave this question. 

mahmud2690:
20161017 09:51:37
Nice problem! 

nsitsk:
20161012 19:00:45
Awesome problem :)


Anant Upadhyay:
20160829 17:16:11
Certainly one of the finest graph problem ! 

sbansalcs:
20160809 08:26:03
Anyone has an online solution? 

hodobox:
20160724 01:54:34
Enjoyed :) 
Added by:  Aditya Muraletharan 
Date:  20130222 
Time limit:  0.143s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  That would be me. 