Buggy python submission (verdict: Time Limit Exceeded):
h,w,m = map(int,input().split())
hw = [[int(i) for i in input().split()] for j in range(m)]

tate = [0]*(w+1)
yoko = [0]*(h+1)

for i in range(m):
    yoko[hw[i][0]] += 1
    tate[hw[i][1]] += 1
    
ans = 0

t_max = -1


for i in range(1,w+1):
    if t_max < tate[i]:
        t_max = tate[i]
        t_max_idx = []
        t_max_idx.append(i)
    elif t_max == tate[i]:
        t_max_idx.append(i)

y_max = -1

for i in range(1,h+1):
    if y_max < yoko[i]:
        y_max = yoko[i]
        y_max_idx = []
        y_max_idx.append(i)
    elif y_max == yoko[i]:
        y_max_idx.append(i)
        
#s_y = set(y_max_idx)
#s_t = set(t_max_idx)

if len(y_max_idx)*len(t_max_idx) > m:
    print(t_max+y_max)
else:
    ans = 0
    for i in range(m):
        if hw[i][0] in y_max_idx and hw[i][1] in t_max_idx:
            ans += 1
    if ans < len(y_max_idx)*len(t_max_idx):
        print(t_max+y_max)
    else:
        print(t_max+y_max-1)

Fixed submission:
h,w,m = map(int,input().split())
hw = [[int(i) for i in input().split()] for j in range(m)]

tate = [0]*(w+1)
yoko = [0]*(h+1)

for i in range(m):
    yoko[hw[i][0]] += 1
    tate[hw[i][1]] += 1
    
ans = 0

t_max = -1


for i in range(1,w+1):
    if t_max < tate[i]:
        t_max = tate[i]
        t_max_idx = []
        t_max_idx.append(i)
    elif t_max == tate[i]:
        t_max_idx.append(i)

y_max = -1

for i in range(1,h+1):
    if y_max < yoko[i]:
        y_max = yoko[i]
        y_max_idx = []
        y_max_idx.append(i)
    elif y_max == yoko[i]:
        y_max_idx.append(i)
        
s_y = set(y_max_idx)
s_t = set(t_max_idx)

if len(y_max_idx)*len(t_max_idx) > m:
    print(t_max+y_max)
else:
    ans = 0
    for i in range(m):
        if hw[i][0] in s_y and hw[i][1] in s_t:
            ans += 1
    if ans < len(y_max_idx)*len(t_max_idx):
        print(t_max+y_max)
    else:
        print(t_max+y_max-1)

Buggy python submission (verdict: Runtime Error):
h,w,m = map(int,input().split())
hw = [[int(i) for i in input().split()] for j in range(m)]

tate = [0]*(w+1)
yoko = [0]*(h+1)

for i in range(m):
    yoko[hw[i][0]] += 1
    tate[hw[i][1]] += 1
    
ans = 0

t_max = -1


for i in range(1,w+1):
    if t_max < tate[i]:
        t_max = tate[i]
        t_max_idx = []
        t_max_idx.append(i)
    elif t_max == tate[i]:
        t_max_idx.append(i)

y_max = -1

for i in range(1,h+1):
    if y_max < yoko[i]:
        y_max = yoko[i]
        y_max_idx = []
        y_max_idx.append(i)
    elif y_max == yoko[i]:
        y_max_idx.append(i)
        
#s_y = set(y_max_idx)
#s_t = set(t_max_idx)

if len(y_max_idx)*len(t_max_idx) > m:
    print(t_max+y_max)
else:
    ans = 0
    for i in range(m):
        if hw[i][0] in s_y and hw[i][1] in s_t:
            ans += 1
    if ans < len(y_max_idx)*len(t_max_idx):
        print(t_max+y_max)
    else:
        print(t_max+y_max-1)

Fixed submission:
h,w,m = map(int,input().split())
hw = [[int(i) for i in input().split()] for j in range(m)]

tate = [0]*(w+1)
yoko = [0]*(h+1)

for i in range(m):
    yoko[hw[i][0]] += 1
    tate[hw[i][1]] += 1
    
ans = 0

t_max = -1


for i in range(1,w+1):
    if t_max < tate[i]:
        t_max = tate[i]
        t_max_idx = []
        t_max_idx.append(i)
    elif t_max == tate[i]:
        t_max_idx.append(i)

y_max = -1

for i in range(1,h+1):
    if y_max < yoko[i]:
        y_max = yoko[i]
        y_max_idx = []
        y_max_idx.append(i)
    elif y_max == yoko[i]:
        y_max_idx.append(i)
        
s_y = set(y_max_idx)
s_t = set(t_max_idx)

if len(y_max_idx)*len(t_max_idx) > m:
    print(t_max+y_max)
else:
    ans = 0
    for i in range(m):
        if hw[i][0] in s_y and hw[i][1] in s_t:
            ans += 1
    if ans < len(y_max_idx)*len(t_max_idx):
        print(t_max+y_max)
    else:
        print(t_max+y_max-1)