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 OCaml (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d %d %d" (fun hh ww m ->
    let module S = Set.Make (struct type t = int let compare = compare end) in
    let module S2 = Set.Make (struct type t = int * int let compare = compare end) in
    let node_h  = Array.make hh S.empty in 
    let node_w  = Array.make ww S.empty in 
    let count_h = Array.make hh 0 in 
    let count_w = Array.make ww 0 in 
    let hw = Array.init m (fun _ -> Scanf.scanf " %d %d" (fun h w -> h - 1, w - 1)) in

    Array.iter (fun (h, w) ->
        node_h.(h)  <- S.add w node_h.(h);
        node_w.(w)  <- S.add h node_w.(w);
        count_h.(h) <- count_h.(h) + 1;
        count_w.(w) <- count_w.(w) + 1;
    ) hw;
    let rec loop_h i set_h =
        if i = hh then set_h else
            loop_h (i + 1) (S2.add (count_h.(i), i) set_h)
    in
    let rec loop_w i set_w =
        if i = ww then set_w else
            loop_w (i + 1) (S2.add (count_w.(i), i) set_w)
    in
    let set_h = loop_h 0 S2.empty in
    let set_w = loop_w 0 S2.empty in

    let ((mch, mih) as mxh) = S2.max_elt set_h in
    let ((mcw, miw) as mxw) = S2.max_elt set_w in

    let rec loop_w w acc =
        if w = ww then acc else
            let cur = if S.mem w node_h.(mih) then mch + count_w.(w) - 1 else mch + count_w.(w) in
            loop_w (w + 1) (max acc cur)
    in
    let acc = loop_w 0 0 in
    let rec loop_h h acc =
        if h = hh then acc else
            let cur = if S.mem h node_w.(miw) then mcw + count_h.(h) - 1 else mcw + count_h.(h) in
            loop_h (h + 1) (max acc cur)
    in
    let acc = loop_h 0 acc in
    Printf.printf "%d\n" acc
)