Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []
PF = defaultdict(int)

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)
    PF[h, w] += 1

frequency_h_list = Counter(PH).most_common()
frequency_w_list = Counter(PW).most_common()
most_common_h_cnt = frequency_h_list[0][1]
most_common_w_cnt = frequency_w_list[0][1]

most_common_h_list = []
for x in frequency_h_list:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in frequency_w_list:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

add = -1
for h in most_common_h_list:
    for w in most_common_w_list:
        if PF[h, w] == 0:
            add = 0

cnt = most_common_h_cnt + most_common_w_cnt + add

print(cnt)

Fixed submission:
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []
PHF = defaultdict(int)
PWF = defaultdict(int)
PF = defaultdict(int)

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)
    PHF[h] += 1
    PWF[w] += 1
    PF[h, w] += 1

sorted_PHF = sorted(PHF.items(), key=lambda x: x[1], reverse=True)
sorted_PWF = sorted(PWF.items(), key=lambda x: x[1], reverse=True)
most_common_h_cnt = sorted_PHF[0][1]
most_common_w_cnt = sorted_PWF[0][1]

most_common_h_list = []
for x in sorted_PHF:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in sorted_PWF:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

add = -1
for h in most_common_h_list:
    for w in most_common_w_list:
        if PF[h, w] == 0:
            add = 0
            break

cnt = most_common_h_cnt + most_common_w_cnt + add

print(cnt)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []
PHF = defaultdict(int)
PWF = defaultdict(int)
PF = defaultdict(int)

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)
    PHF[h] += 1
    PWF[w] += 1
    PF[h, w] += 1

sorted_PHF = sorted(PHF.items(), key=lambda x: x[1], reverse=True)
sorted_PWF = sorted(PWF.items(), key=lambda x: x[1], reverse=True)
most_common_h_cnt = sorted_PHF[0][1]
most_common_w_cnt = sorted_PWF[0][1]

most_common_h_list = []
for x in sorted_PHF:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in sorted_PWF:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

add = -1
for h in most_common_h_list:
    for w in most_common_w_list:
        if PF[h, w] == 0:
            add = 0

cnt = most_common_h_cnt + most_common_w_cnt + add

print(cnt)

Fixed submission:
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []
PHF = defaultdict(int)
PWF = defaultdict(int)
PF = defaultdict(int)

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)
    PHF[h] += 1
    PWF[w] += 1
    PF[h, w] += 1

sorted_PHF = sorted(PHF.items(), key=lambda x: x[1], reverse=True)
sorted_PWF = sorted(PWF.items(), key=lambda x: x[1], reverse=True)
most_common_h_cnt = sorted_PHF[0][1]
most_common_w_cnt = sorted_PWF[0][1]

most_common_h_list = []
for x in sorted_PHF:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in sorted_PWF:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

add = -1
for h in most_common_h_list:
    for w in most_common_w_list:
        if PF[h, w] == 0:
            add = 0
            break

cnt = most_common_h_cnt + most_common_w_cnt + add

print(cnt)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)

frequency_h_list = Counter(PH).most_common()
frequency_w_list = Counter(PW).most_common()
most_common_h_cnt = frequency_h_list[0][1]
most_common_w_cnt = frequency_w_list[0][1]

most_common_h_list = []
for x in frequency_h_list:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in frequency_w_list:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

contain_intersection = {}
for h in most_common_h_list:
    for w in most_common_w_list:
        contain_intersection[h, w] = False

for i in range(M):
    h, w = PH[i], PW[i]
    if (h, w) in contain_intersection:
        contain_intersection[h, w] = True
cnt = most_common_h_cnt + most_common_w_cnt
if all([contain_intersection[key] for key in contain_intersection]):
    cnt -= 1

print(cnt)

Fixed submission:
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []
PHF = defaultdict(int)
PWF = defaultdict(int)
PF = defaultdict(int)

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)
    PHF[h] += 1
    PWF[w] += 1
    PF[h, w] += 1

sorted_PHF = sorted(PHF.items(), key=lambda x: x[1], reverse=True)
sorted_PWF = sorted(PWF.items(), key=lambda x: x[1], reverse=True)
most_common_h_cnt = sorted_PHF[0][1]
most_common_w_cnt = sorted_PWF[0][1]

most_common_h_list = []
for x in sorted_PHF:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in sorted_PWF:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

add = -1
for h in most_common_h_list:
    for w in most_common_w_list:
        if PF[h, w] == 0:
            add = 0
            break

cnt = most_common_h_cnt + most_common_w_cnt + add

print(cnt)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
INF = 10**18
sys.setrecursionlimit(10**6)
def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = [0] * (3 * (10 ** 5))
PW = [0] * (3 * (10 ** 5))
for i in range(M):
    h, w = li()
    PH[i] = h
    PW[i] = w

mh = max(PH, key=PH.count)
mw = max(PW, key=PW.count)

is_same = False
for i in range(M):
    if PH[i] == mh and PW[i] == mw:
        is_same = True
cnt = PH.count(mh) + PW.count(mw)
if is_same:
    cnt -= 1

print(cnt)

Fixed submission:
from collections import Counter
from collections import defaultdict

def li():
    return [int(x) for x in input().split()]

H, W, M = li()
PH = []
PW = []
PHF = defaultdict(int)
PWF = defaultdict(int)
PF = defaultdict(int)

for i in range(M):
    h, w = li()
    PH.append(h)
    PW.append(w)
    PHF[h] += 1
    PWF[w] += 1
    PF[h, w] += 1

sorted_PHF = sorted(PHF.items(), key=lambda x: x[1], reverse=True)
sorted_PWF = sorted(PWF.items(), key=lambda x: x[1], reverse=True)
most_common_h_cnt = sorted_PHF[0][1]
most_common_w_cnt = sorted_PWF[0][1]

most_common_h_list = []
for x in sorted_PHF:
    if x[1] < most_common_h_cnt:
        break
    most_common_h_list.append(x[0])

most_common_w_list = []
for x in sorted_PWF:
    if x[1] < most_common_w_cnt:
        break
    most_common_w_list.append(x[0])

add = -1
for h in most_common_h_list:
    for w in most_common_w_list:
        if PF[h, w] == 0:
            add = 0
            break

cnt = most_common_h_cnt + most_common_w_cnt + add

print(cnt)