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 Julia (1.4.0) (judge verdict: Runtime Error)

function main()
    H,W,M = reads(Int,Int,Int)
    hc = zeros(Int, H)
    wc = zeros(Int, W)
    hwset = Set(Tuple{Int,Int}[])
    for i in 1:M
        hi,wi = reads(Int,Int)
        push!(hwset, (hi,wi))
        hc[hi] += 1
        wc[wi] += 1
    end
    mhi = [1]
    mhv = hc[1]
    for i in 2:H
        if mhv < hc[i]
            mhi = i
            mhv = hc[i]
        elseif mhv == hc[i]
            push!(mhi, i)
        end
    end
    mwi = [1]
    mwv = wc[1]
    for i in 2:W
        if mwv < wc[i]
            mwi = [i]
            mwv = wc[i]
        elseif mwv == wc[i]
            push!(mwi, i)
        end
    end
    for i in mhi, j in mwi
        if !((i,j) in hwset)
            println(mhv+mwv)
            return
        end
    end
    println(mhv+mwv-1)
end

import Base.parse
import Base.StringVector

parse(::Type{String},  str::AbstractString) = str
isdelim(x::UInt8, xs::Set{UInt8}) = x in xs
const delimset = Set([0x0a, 0x20])

function myreaduntil(s::IO, delims::Set{UInt8})::Vector{UInt8}
    out = StringVector(0)
    c::UInt8 = 0x00
    while !eof(s)
        c = read(s, UInt8)
        !isdelim(c, delims) && break
    end
    push!(out, c)
    eof(s) && return out
    while !eof(s)
        c = read(s, UInt8)
        isdelim(c, delims) && break
        push!(out, c)
    end
    return out
end

function readword(io::IO = stdin, delims = delimset)::String
    word = myreaduntil(io, delims)
    i = length(word)
    if i == 0 || word[i] != 0x0a
        return String(word)
    elseif i < 2 || word[i-1] != 0x0d
        return String(resize!(word,i-1))
    else
        return String(resize!(word,i-2))
    end
end

pread(ty) = parse(ty, readword())

reads(tys...)::Tuple{tys...} = Tuple{tys...}(pread(ty) for ty in tys)

function readvec(tys::Tuple , len::Signed)::Tuple{map(x -> Vector{x},tys)...}
    rv = Tuple{map(x -> Vector{x},tys)...}(Vector{ty}(undef,len) for ty in tys)
    for i in 1:len
        for j in 1:length(tys)
            @inbounds rv[j][i] = pread(tys[j])
        end
    end
    rv
end

readvec(ty::Type, len::Signed)::Vector{ty} = @inbounds ty[pread(ty) for i in 1:len]

function readmat(ty::Type, s...)::Matrix{ty}
    v = Matrix{ty}(undef, s...)
    @inbounds for i in 1:s[1]
        v[i,:] = readvec(ty, s[2])
    end
    v
end

main()