Problem Statement

Jen is playing a card game with \(W \times H\) cards.
Jen wants to know the number of cards outside her hand that match any of the cards in her hand (whose faces she can see).

This deck has \(W\) kinds of suits and numbers from \(1\) to \(H\), and no combination is duplicated.
Here, a card matches if either its suit or its number is the same.

There are now \(N\) cards in her hand. Find the number of matching cards among "the cards other than those in her hand".

\(W \times H\) may be \(2^{32}\) or greater.

Input

\(W\)
\(H\)
\(N\)
\(S_1\ K_1\)
\(S_2\ K_2\)
\(\dots\)
\(S_i\ K_i\)
\(\dots\)
\(S_N\ K_N\)

The \(1\)st line contains an integer \(W\ (1 \leq W \leq 1,000,000) \), the number of kinds of suits in the deck.
The \(2\)nd line contains an integer \(H\ (1 \leq H \leq 1,000,000) \), the maximum number in the deck.
The \(3\)rd line contains an integer \(N\ (1 \leq N \leq min(W \times H, 100)) \), the number of cards in her hand.
Each of the following \(N\) lines contains \(S_i\ (1 \leq S_i \leq W) \) and \(K_i\ (1 \leq K_i \leq H) \), separated by a space, representing the suit and number of a card in her hand.
It is guaranteed that when $i \neq j$, the pairs of values $(S_i, K_i)$ and $(S_j, K_j)$ are different.

Output

Output the number of matching cards among "the cards other than those in her hand".

Sample

2
5
1
1 1

5

4
13
3
1 1
2 1
2 5

27

4
13
4
1 5
2 6
3 7
4 8

48

3
2
2
1 1
2 1

3