Syrjälä's network has $n$ computers and $m$ connections between them. The network consists of components of computers that can send messages to each other.
Nobody in Syrjälä understands how the network works. For this reason, if a connection breaks down, nobody will repair it. In this situation a component may be divided into two components.
Your task is to calculate the number of components after each connection breakdown.
The first input line has three integers $n$ , $m$ and $k$ : the number of computers, connections and breakdowns. The computers are numbered $1,2,\dots,n$ .
Then, there are $m$ lines describing the connections. Each line has two integers $a$ and $b$ : there is a connection between computers $a$ and $b$ . Each connection is between two different computers, and there is at most one connection between two computers.
Finally, there are $k$ lines describing the breakdowns. Each line has two integers $a$ and $b$ : the connection between computers $a$ and $b$ breaks down.
After each breakdown, print the number of components.
5 5 3 1 2 1 3 2 3 3 4 4 5 3 4 2 3 4 5· · \n · \n · \n · \n · \n · \n · \n · \n · \n
2 2 3· · \n