CSES Problem Set

# Network Breakdown

CSES - Network BreakdownCSES - 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