CSES - Network Breakdown
  • Time limit: 1.00 s
  • Memory limit: 512 MB
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.

Input

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.

Output

After each breakdown, print the number of components.

Constraints
  • $1 \le n \le 10^5$
  • $1 \le m \le 2 \cdot 10^5$
  • $1 \le k \le m$
  • $1 \le a,b \le n$
Example

Input:
5 5 3
1 2
1 3
2 3
3 4
4 5
3 4
2 3
4 5


Output:
2 2 3