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
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 :) 

ASHUTOSH DWIVEDI:
20160621 23:45:25
'Kudos' to the problem setter :) 

shikhar0037:
20160521 13:07:02
One of the finest graph problem . AC in 1 go :) 

torque:
20151230 13:00:33
Great problem!! 

free mind ;):
20150912 11:10:22
#15115856 can you look into this solution . can you give me test case , where my solution is failing. please 

Rishav Goyal:
20150712 21:14:47
Cool problem 

Aayush Agarwal:
20140528 00:18:52
Awesome problem ! 

Rana Saha:
20140419 10:49:59
Nice Problem! :) 
Added by:  Aditya Muraletharan 
Date:  20130222 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  That would be me. 