Problem:
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

Output

Print the answer.

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

Solution in Lua (Lua 5.3.5) (judge verdict: Wrong Answer)

local read = io.read
local insert = table.insert

local h, w, m = read("n", "n", "n")
local grid_t = {}
for i = 1, h do
	grid_t[i] = {}
end

local sum_h_t, sum_w_t = {}, {}
for i = 1, m do
	local hs = read("n")
	local ws = read("n")
	grid_t[hs][ws] = true
	sum_h_t[hs] = sum_h_t[hs] and sum_h_t[hs] + 1 or 1
	sum_w_t[ws] = sum_w_t[ws] and sum_w_t[ws] + 1 or 1
end

local max_h, max_w = 0, 0
local max_h_index_t, max_w_index_t = {}, {}
for i = 1, w do
	if sum_h_t[i] and sum_h_t[i] > max_h then
		max_h = sum_h_t[i]
		max_h_index_t = {i}
	elseif sum_h_t[i] and sum_h_t[i] == max_h then
		insert(max_h_index_t, i)
	end
end
for i = 1, h do
	if sum_w_t[i] and sum_w_t[i] > max_w then
		max_w = sum_w_t[i]
		max_w_index_t = {i}
	elseif sum_w_t[i] and sum_w_t[i] == max_w then
		insert(max_w_index_t, i)
	end
end

local is_dup = true
for i = 1, #max_h_index_t do
	for j = 1, #max_w_index_t do
		if grid_t[max_h_index_t[i]][max_w_index_t[j]] == nil then
			is_dup = false
			break
		end
	end
	if not is_dup then
		break
	end
end

print(is_dup and max_h + max_w - 1 or max_h + max_w)