Buggy python submission (verdict: Time Limit Exceeded):
H, W, M = map(int, input().split())
h_dic, w_dic = {}, {}
m = set()
for i in range(M):
    h_i, w_i = map(int, input().split())
    m.add((h_i, w_i))
    if h_i in h_dic:
        h_dic[h_i] += 1
    else:
        h_dic[h_i] = 1
    if w_i in w_dic:
        w_dic[w_i] += 1
    else:
        w_dic[w_i] = 1
        
max_h_items = [[0,0]]
max_w_items = [[0,0]]

for key, value in h_dic.items():
    if value > max_h_items[0][1]:
        max_h_items = [[key, value]]
    elif value == max_h_items[0][1]:
        max_h_items.append([key, value])
for key, value in w_dic.items():
    if value > max_w_items[0][1]:
        max_w_items = [[key, value]]
    elif value == max_w_items[0][1]:
        max_w_items.append([key, value])
s = max_h_items[0][1] + max_w_items[0][1] - 1
for mh in max_h_items:
    for mw in max_w_items:
        if (mh[0], mw[0]) not in m:
            s = mh[1]+mw[1]
print(s)

Fixed submission:
H, W, M = map(int, input().split())
h_dic, w_dic = {}, {}
m = set()
for i in range(M):
    h_i, w_i = map(int, input().split())
    m.add((h_i, w_i))
    if h_i in h_dic:
        h_dic[h_i] += 1
    else:
        h_dic[h_i] = 1
    if w_i in w_dic:
        w_dic[w_i] += 1
    else:
        w_dic[w_i] = 1
        
max_h_items = [[0,0]]
max_w_items = [[0,0]]

for key, value in h_dic.items():
    if value > max_h_items[0][1]:
        max_h_items = [[key, value]]
    elif value == max_h_items[0][1]:
        max_h_items.append([key, value])
for key, value in w_dic.items():
    if value > max_w_items[0][1]:
        max_w_items = [[key, value]]
    elif value == max_w_items[0][1]:
        max_w_items.append([key, value])
s = max_h_items[0][1] + max_w_items[0][1] - 1
for mh in max_h_items:
    for mw in max_w_items:
        if (mh[0], mw[0]) not in m:
            s = mh[1]+mw[1]
            print(s)
            break
    if s == max_h_items[0][1] + max_w_items[0][1]:
        break
if s == max_h_items[0][1] + max_w_items[0][1] - 1:
    print(s)

Buggy python submission (verdict: Time Limit Exceeded):
H, W, M = map(int, input().split())
h, w = [], []
h_dic, w_dic = {}, {}

for i in range(M):
    h_i, w_i = map(int, input().split())
    h.append(h_i)
    w.append(w_i)
    if h_i in h_dic:
        h_dic[h_i] += 1
    else:
        h_dic[h_i] = 1
    if w_i in w_dic:
        w_dic[w_i] += 1
    else:
        w_dic[w_i] = 1
        
max_h_items = [[0,0]]
max_w_items = [[0,0]]

for key, value in h_dic.items():
    if value > max_h_items[0][1]:
        max_h_items = [[key, value]]
    elif value == max_h_items[0][1]:
        max_h_items.append([key, value])
for key, value in w_dic.items():
    if value > max_w_items[0][1]:
        max_w_items = [[key, value]]
    elif value == max_w_items[0][1]:
        max_w_items.append([key, value])

max_count = 0
for mh in max_h_items:
    for mw in max_w_items:
        count = 0
        for i in range(M):
            if h[i] == mh[0] or w[i] == mw[0]:
                count += 1
        max_count = max(max_count, count)
print(max_count)

Fixed submission:
H, W, M = map(int, input().split())
h_dic, w_dic = {}, {}
m = set()
for i in range(M):
    h_i, w_i = map(int, input().split())
    m.add((h_i, w_i))
    if h_i in h_dic:
        h_dic[h_i] += 1
    else:
        h_dic[h_i] = 1
    if w_i in w_dic:
        w_dic[w_i] += 1
    else:
        w_dic[w_i] = 1
        
max_h_items = [[0,0]]
max_w_items = [[0,0]]

for key, value in h_dic.items():
    if value > max_h_items[0][1]:
        max_h_items = [[key, value]]
    elif value == max_h_items[0][1]:
        max_h_items.append([key, value])
for key, value in w_dic.items():
    if value > max_w_items[0][1]:
        max_w_items = [[key, value]]
    elif value == max_w_items[0][1]:
        max_w_items.append([key, value])
s = max_h_items[0][1] + max_w_items[0][1] - 1
for mh in max_h_items:
    for mw in max_w_items:
        if (mh[0], mw[0]) not in m:
            s = mh[1]+mw[1]
            print(s)
            break
    if s == max_h_items[0][1] + max_w_items[0][1]:
        break
if s == max_h_items[0][1] + max_w_items[0][1] - 1:
    print(s)