Problem Statement

In the Kingdom of harurun, there are $N$ men numbered $1\sim N$ and $M$ women numbered $1\sim M$.

The king, harurun, wants to form as many man-woman pairs as possible.

When pairs are formed so that all of the following conditions are satisfied, what is the maximum number of pairs that can be formed?

Conditions

• The same person cannot belong to multiple pairs.

• Arrays $a,b$ of $Q$ elements are given. Man $x$ and woman $y$ can form a pair only when there exists an $i$ such that $a_i=x$, $b_i=y$.

• Let $C_i=(x_i,y_i)$ be the $i$-th pair formed. If $i<j$, then $x_i<x_j$ and $y_i<y_j$ must hold. ($x_i$ represents a man and $y_i$ represents a woman.)

Input

$N\ M\ Q$
$a_1\ b_1$
$\vdots$
$a_Q\ b_Q$

• Line $1$ contains $N$,$M$,$Q$ separated by spaces.

• Lines $2\sim Q+1$ contain $a_i$,$b_i$ separated by spaces.

Constraints

• $1≤N,M≤10^3$

• $1≤Q≤N\times M$

• $1≤a_i≤N$

• $1≤b_i≤M$

• $(a_i,b_i)\neq(a_j,b_j)$ when $i\neq j$

• All inputs are integers.

Output

Output the answer on one line. Print a newline at the end.

Sample

1 1 1
1 1

1

3 3 2
1 2
2 3

2

3 3 3
1 2
2 3
3 1

2