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E - Bomber /

Time Limit: 3 sec / Memory Limit: 1024 MB

問題文

H \times W マスの二次元グリッドがあります。この中には M 個の爆破対象があります。 i 個目の爆破対象の位置は \left(h_i, w_i \right)です。

制約

• 入力は全て整数
• 1 \leq H, W \leq 3 \times 10^5
• 1 \leq M \leq \min\left(H\times W, 3 \times 10^5\right)
• 1 \leq h_i \leq H
• 1 \leq w_i \leq W
• \left(h_i, w_i\right) \neq \left(h_j, w_j\right) \left(i \neq j\right)

入力

H W M
h_1 w_1
\vdots
h_M w_M


入力例 1

2 3 3
2 2
1 1
1 3


出力例 1

3


入力例 2

3 3 4
3 3
3 1
1 1
1 2


出力例 2

3


入力例 3

5 5 10
2 5
4 3
2 3
5 5
2 2
5 4
5 3
5 1
3 5
1 4


出力例 3

6


Score : 500 points

Problem Statement

We have a two-dimensional grid with H \times W squares. There are M targets to destroy in this grid - the position of the i-th target is \left(h_i, w_i \right).

Takahashi will choose one square in this grid, place a bomb there, and ignite it. The bomb will destroy all targets that are in the row or the column where the bomb is placed. It is possible to place the bomb at a square with a target.

Takahashi is trying to maximize the number of targets to destroy. Find the maximum number of targets that can be destroyed.

Constraints

• All values in input are integers.
• 1 \leq H, W \leq 3 \times 10^5
• 1 \leq M \leq \min\left(H\times W, 3 \times 10^5\right)
• 1 \leq h_i \leq H
• 1 \leq w_i \leq W
• \left(h_i, w_i\right) \neq \left(h_j, w_j\right) \left(i \neq j\right)

Input

Input is given from Standard Input in the following format:

H W M
h_1 w_1
\vdots
h_M w_M


Sample Input 1

2 3 3
2 2
1 1
1 3


Sample Output 1

3


We can destroy all the targets by placing the bomb at \left(1, 2\right).

Sample Input 2

3 3 4
3 3
3 1
1 1
1 2


Sample Output 2

3


Sample Input 3

5 5 10
2 5
4 3
2 3
5 5
2 2
5 4
5 3
5 1
3 5
1 4


Sample Output 3

6