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 (Python):
def main():
    import sys
    from collections import defaultdict
    readline = sys.stdin.readline

    H, W, M = map(int, readline().rstrip().split())
    HB = [0] * H
    WB = [0] * W
    HW = defaultdict(lambda : False)
    for _ in range(M):
        h, w = map(int, readline().rstrip().split())
        h -= 1
        w -= 1
        HW[(h,w)] = True
        HB[h] += 1
        WB[w] += 1
    hb = max(HB)
    max_h = [i for i, x in enumerate(HB) if x == hb]
    wb = max(WB)
    max_w = [i for i, x in enumerate(WB) if x == wb]
    
    ans = hb + wb
    for mh in max_h:
        for mw in max_w:
            if HW[(mh, mw)] == False:
                print(ans)
                sys.exit(0)
    print(ans - 1)

if __name__ == "__main__":
    main()

Solution (Python):
H,W,M=map(int,input().split())
L=[0 for _ in range(H)]
C=[0 for _ in range(W)]
B={}
for _ in range(M):
    a,b=map(int,input().split())
    B[str(a)+","+str(b)]=0
    L[a-1]+=1
    C[b-1]+=1

LM=max(L)
CM=max(C)

l=[]
c=[]
for j in range(H):
    if L[j]==LM:
        l.append(j)

for k in range(W):
    if C[k]==CM:
        c.append(k)

ans=LM+CM-1

for a in l:
    for b in c:
        if str(a+1)+","+str(b+1) not in B:
            ans=LM+CM
            break
    if ans==LM+CM:
        break
print(ans)

Solution (Python):
H,W,M = map(int,input().split())
Bomb = []
H_num = [0 for _ in range(H)]
W_num = [0 for _ in range(W)]
for i in range(M):
  a,b = map(int,input().split())
  a-=1;b-=1
  Bomb.append([a,b])
  H_num[a] += 1
  W_num[b] += 1

HMAX = max(H_num);WMAX = max(W_num)
ans = HMAX+WMAX
HMAX_list = set([]); WMAX_list = set([])
for i in range(H):
  if H_num[i] == HMAX:
    HMAX_list.add(i)
for i in range(W):
  if W_num[i] == WMAX:
    WMAX_list.add(i)
kosu = len(HMAX_list)*len(WMAX_list)
cnt = 0
for z in Bomb:
  x = z[0];y = z[1]
  if x in HMAX_list and y in WMAX_list:
    cnt += 1

if cnt < kosu:
  print(ans)
else:
  print(ans-1)

Solution (Python):

(h, w, m), *s = [[*map(int, i.split())] for i in open(0)]
r = [0] * (h + 1)
c = [0] * (w + 1)
for x, y in s:
    r[x] += 1
    c[y] += 1
R = max(r)
nr = {i for i, x in enumerate(r) if x == R}
C = max(c)
nc = {i for i, x in enumerate(c) if x == C}
count = sum(x in nr and y in nc for x, y in s)
print(R + C - (len(nr) * len(nc) == count))

Solution (Python):
import sys
import math
import itertools
import collections
from collections import deque
from collections import defaultdict

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
input = lambda: sys.stdin.readline().strip()

NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()

def main():
    N, W, M = NMI()
    
    BOMB_HW = [NLI() for _ in range(M)]
    
    bomb_h,bomb_w = zip(*BOMB_HW)
    
    dd = defaultdict(bool)
    for m in range(M):
        dd[str(bomb_h[m]) + "-" + str(bomb_w[m])] = True
    
    c_h = collections.Counter(bomb_h)
    c_w = collections.Counter(bomb_w)
    
    bomb_most_h = c_h.most_common()[0]
    bomb_most_w = c_w.most_common()[0]

    bh_destroy = bomb_most_h[1]
    bw_destroy = bomb_most_w[1]
 
    candidate_h = [i[0] for i in c_h.items() if i[1] == bh_destroy]
    candidate_w = [i[0] for i in c_w.items() if i[1] == bw_destroy]

    ans = bh_destroy+bw_destroy
    

    for bh in candidate_h:
        for bw in candidate_w:   
            if not(dd[str(bh) + "-" + str(bw)]):
                print(ans)
                sys.exit()
    print(ans-1)
    


if __name__ == '__main__':
    main()

Solution (Python):
f=lambda:map(int,input().split())
h,w,m=f()
l,H,W=[],[0]*-~h,[0]*-~w
for _ in range(m):
  x,y=f()
  l+=[(x,y)]
  H[x]+=1
  W[y]+=1
s,t=max(H),max(W)
print(s+t-(H.count(s)*W.count(t)==sum(H[x]+W[y]==s+t for x,y in l)))

Solution (Python):
H,W,M = map(int,input().split())
lsx = [0] + [0]*H
lsy = [0] + [0]*W
lsxy = []
for i in range(M):
    x,y = map(int,input().split())
    lsx[x] += 1
    lsy[y] += 1
    lsxy.append([x,y])
maxx = max(lsx)
maxy = max(lsy)
cx = lsx.count(maxx)
cy = lsy.count(maxy)
al = cx*cy
for i in range(M):
    if lsx[lsxy[i][0]] == maxx and lsy[lsxy[i][1]] == maxy:
        al -= 1
if al == 0:
    factor = 1
else:
    factor = 0        
print(maxx+maxy-factor)

Solution (Python):
h, w, m = map(int, input().split())
boms = set()
Hs = [0] * h
Ws = [0] * w
for i in range(m):
  _h, _w = map(int, input().split())
  boms.add((_h - 1, _w - 1))
  Hs[_h - 1] += 1
  Ws[_w - 1] += 1
Hmax = max(Hs)
Hcount = Hs.count(Hmax)
Wmax = max(Ws)
Wcount = Ws.count(Wmax)
Hindexs = [0] * Hcount
Windexs = [0] * Wcount
hcount = 0
wcount = 0
for i in range(h):
  if Hs[i] == Hmax:
    Hindexs[hcount] = i
    hcount += 1
for i in range(w):
  if Ws[i] == Wmax:
    Windexs[wcount] = i
    wcount += 1
if m < len(Hindexs) * len(Windexs):
  print(Hmax + Wmax)
  exit()
for hindex in Hindexs:
  for windex in Windexs:
    if (hindex,windex) not in boms: 
      print(Hmax + Wmax)
      exit()
print(Hmax + Wmax -1)

Solution (Python):
H, W, M = map(int, input().split())
lh = [0]*(H+1)
lw = [0]*(W+1)
l = []
for _ in range(M):
  h, w = map(int, input().split())
  lh[h] += 1
  lw[w] += 1
  l += [[h, w]]

maxh = max(lh)
maxw = max(lw)
cnt = 0

ch = lh.count(maxh)
cw = lw.count(maxw)
for y, x in l:
  if lh[y] == maxh and lw[x] == maxw:
    cnt += 1

ans = maxh+maxw
if cnt == ch*cw:
  ans -= 1

print(ans)

Solution (Python):
h, w, m =  map(int, input().split())
bom_list = []
h_list = [0] * h
w_list = [0] * w

for i in range(m):
    a, b =  map(int, input().split())
    bom_list.append([a - 1, b - 1])
    h_list[a - 1] += 1
    w_list[b - 1] += 1

max_h = max(h_list)
max_w = max(w_list)
ans = max_h + max_w
count = 0

for bom in bom_list:
    if h_list[bom[0]] == max_h and w_list[bom[1]] == max_w:
        count += 1

if h_list.count(max_h) * w_list.count(max_w) == count:
    ans -= 1

print(ans)

Solution (Python):
ans=0

h,w,m=map(int,input().split())
d=list()
from collections import defaultdict
r=defaultdict(int)
c=defaultdict(int)
r=[0]*(h+1)
c=[0]*(w+1)
for i in range(m):
  a,b=map(int,input().split())
  d+=(a,b),
  r[a]+=1
  c[b]+=1
R=max(r)
C=max(c)

x=0
nr=r.count(R)
nc=c.count(C)
for i in range(m):
    a,b=d[i]
    if r[a]==R and c[b]==C:
        x+=1

ans=R+C
if x==nr*nc:
    ans-=1
print(ans)

Solution (Python):
import itertools
H,W,m = map(int,input().split())
hs = [0 for _ in range(H)]
ws = [0 for _ in range(W)]
data = set()

for j in range(m):
	h,w = map(int,input().split())
	data.add((h-1, w-1))
	hs[h-1] += 1
	ws[w-1] += 1



maxhs = 0
maxws = 0
maxhsindex = []
maxwsindex = []

for i in range(H):
	targ = hs[i]
	if targ > maxhs:
		maxhs = targ
		maxhsindex = [i]
	elif targ == maxhs:
		maxhsindex.append(i)

for i in range(W):
	targ = ws[i]
	if targ > maxws:
		maxws = targ
		maxwsindex = [i]
	elif targ == maxws:
		maxwsindex.append(i)


for i, j in itertools.product(maxhsindex, maxwsindex):
	
	if (i, j) not in data:
		print(max(hs)+max(ws))
		exit()
print(max(hs)+max(ws)-1)

Solution (Python):
from collections import defaultdict


def main():
    height, width, target_count = [int(x) for x in input().split()]
    count_by_height = defaultdict(int)
    count_by_width = defaultdict(int)
    bomb_is = set()
    for _ in range(target_count):
        bom_h, bom_w = [int(x) - 1 for x in input().split()]
        count_by_height[bom_h] += 1
        count_by_width[bom_w] += 1
        bomb_is.add((bom_h, bom_w))
    max_h = max(v for v in count_by_height.values())
    max_w = max(v for v in count_by_width.values())
    max_h_index = [i for i, x in count_by_height.items() if x == max_h]
    max_w_index = [i for i, x in count_by_width.items() if x == max_w]
    no_cross = any(
        (hh, ww) not in bomb_is for hh in max_h_index for ww in max_w_index)
    return max_h + max_w - (not no_cross)


if __name__ == '__main__':
    ans = main()
    print(ans)

Solution (Python):

h, w, m = map(int, input().split())
r = [0] * (h + 1)
c = [0] * (w + 1)
s = []
for _ in range(m):
    x, y = map(int, input().split())
    r[x] += 1
    c[y] += 1
    s.append([x, y])
R = max(r)
nr = {i for i, x in enumerate(r) if x == R}
C = max(c)
nc = {i for i, x in enumerate(c) if x == C}
count = 0
for x, y in s:
    count += x in nr and y in nc
print(R + C - (len(nr) * len(nc) == count))

Solution (Python):
import sys
H, W, M = map(int, sys.stdin.readline().split())
hlst = {}
wlst = {}
hwlst = []

for i in range(M):
    h, w = sys.stdin.readline().split()
    if h in hlst:
        hlst[h] += 1
    else:
        hlst[h] = 1

    if w in wlst:
        wlst[w] += 1
    else:
        wlst[w] = 1

    hwlst.append([h, w])

h = max(hlst.values())
w = max(wlst.values())
hmax = [i for i in hlst if hlst[i] == h]
wmax = [i for i in wlst if wlst[i] == w]
num = len(hmax)*len(wmax)
ans = h + w -1


for i in hwlst:
    if hlst[i[0]] == h and wlst[i[1]] == w:
        num -= 1

if num == 0:
    print(h+w-1)
else:
    print(h+w)

Solution (Python):

import collections

H, W, M = map(int, input().split())
tate = []
yoko = []
S = set()

for i in range(M):
    h, w = map(int, input().split())
    tate.append(h-1)
    yoko.append(w-1)
    S.add((h-1, w-1))

tate = collections.Counter(tate)
yoko = collections.Counter(yoko)
yoko_max = yoko.most_common()[0][1]
yoko_index = []
tate_max = tate.most_common()[0][1]
tate_index = []

for k, v in yoko.most_common():
    if v == yoko_max: yoko_index.append(k)
    else: break

for k, v in tate.most_common():
    if v == tate_max: tate_index.append(k)
    else: break

for i in yoko_index:
    for j in tate_index:
        if (j, i) in S:
            continue
        else:
            print(tate_max + yoko_max)
            exit()


print(tate_max + yoko_max - 1)

Solution (Python):
h, w, m = map(int, input().split())
boms = set()
Hs = [0] * h
Ws = [0] * w
for i in range(m):
  _h, _w = map(int, input().split())
  boms.add((_h - 1, _w - 1))
  Hs[_h - 1] += 1
  Ws[_w - 1] += 1
Hmax = max(Hs)
Hcount = Hs.count(Hmax)
Wmax = max(Ws)
Wcount = Ws.count(Wmax)
Hindexs = [0] * Hcount
Windexs = [0] * Wcount
hcount = 0
wcount = 0
for i in range(h):
  if Hs[i] == Hmax:
    Hindexs[hcount] = i
    hcount += 1
for i in range(w):
  if Ws[i] == Wmax:
    Windexs[wcount] = i
    wcount += 1
if m < len(Hindexs) * len(Windexs):
  print(Hmax + Wmax)
  exit()
for hindex in Hindexs:
  for windex in Windexs:
    if (hindex,windex) not in boms: 
      print(Hmax + Wmax)
      exit()
print(Hmax + Wmax -1)

Solution (Python):


def main():
    H, W, M = map(int, input().split())
    bomb = [list(map(int, input().split()))for i in range(M)]
    H_bomb = [0] * (H + 1)
    W_bomb = [0] * (W + 1)
    for b in bomb:
        H_bomb[b[0]] += 1
        W_bomb[b[1]] += 1
    max_h, max_w = max(H_bomb), max(W_bomb)
    cnt = H_bomb.count(max_h) * W_bomb.count(max_w)
    for b in bomb:
        if H_bomb[b[0]] == max_h and W_bomb[b[1]] == max_w:
            cnt -= 1
    print(max_h + max_w + bool(cnt) - 1)


if __name__ == "__main__":
    main()

Solution (Python):

from collections import defaultdict
import sys

H, W, M = (int(x) for x in input().split())

NH = [[0, i] for i in range(H)]
NW = [[0, i] for i in range(W)]

B = defaultdict(int) 
for i in range(M):
    h, w = (int(x)-1 for x in input().split())
    B[(h, w)] = 0
    NH[h][0] += 1
    NW[w][0] += 1

NH.sort(reverse=True)
NW.sort(reverse=True)
maxH = NH[0][0]
maxW = NW[0][0]

for i in range(H):
    countH, idxH = NH[i] 
    if countH != maxH:
        break

    for j in range(W):
        countW, idxW = NW[j] 
        if countW!= maxW:
            break

        if (idxH, idxW) not in B:
            print(maxH + maxW)
            sys.exit(0)

print(maxH + maxW - 1)

Solution (Python):
import numpy as np

[H, W, M] = map(int, input().split())
colsum = np.zeros(W+1)
rowsum = np.zeros(H+1)
bombs = []
rowbombs = [set() for i in range(H+1)]
for i in range(M):
    [h, w] = map(int, input().split())
    rowsum[h] += 1
    colsum[w] += 1
    bombs.append([h, w])
    rowbombs[h].add(w)

maxcol = max(colsum)
maxrow = max(rowsum)

colchk = np.where(colsum==maxcol)
rowchk = np.where(rowsum==maxrow)

for i in range(len(rowchk[0])):
    for j in range(len(colchk[0])):
        if colchk[0][j] not in rowbombs[rowchk[0][i]]:
            print(int(max(colsum)+max(rowsum)))
            quit()

print(int(max(colsum)+max(rowsum))-1)

Solution (Python):
import sys
input = sys.stdin.readline

h, w, m = map(int, input().split())
hw = [list(map(int, input().split())) for _ in range(m)]

ch = [[0, i] for i in range(h)]
cw = [[0, i] for i in range(w)]
ngh = {}
ngw = {}

for h, w in hw:
    ch[h-1][0] += 1
    cw[w-1][0] += 1

ch.sort(key=lambda x: x[0], reverse=True)
cw.sort(key=lambda x: x[0], reverse=True)
mch = ch[0][0]
mcw = cw[0][0]

for cnt, i in ch:
    if cnt == mch:
        ngh[i] = 1
    else:
        break

for cnt, i in cw:
    if cnt == mcw:
        ngw[i] = 1
    else:
        break

cnt = 0
for h, w in hw:
    if h-1 in ngh and w-1 in ngw:
        cnt += 1

lenh = len(list(ngh.keys()))
lenw = len(list(ngw.keys()))

if lenh * lenw == cnt:
    print(mch + mcw -1)
else:
    print(mch + mcw)

Solution (Python):
from bisect import bisect_left
import sys
input = sys.stdin.readline
H,W,m = map(int,input().split())
h = [0]*(H+1)
w = [0]*(W+1)
c = [[-1,10**6] for i in range(H+1)]
for i in range(m):
    a,b = map(int,input().split())
    h[a] += 1
    w[b] += 1
    c[a].append(b)
mh = max(h)
mw = max(w)
hkouho = []
wkouho = []
for i in range(H+1):
    if h[i] == mh:
        hkouho.append(i)
for i in range(W+1):
    if w[i] == mw:
        wkouho.append(i)
for i in hkouho:
    c[i].sort()
    for j in wkouho:
        if c[i][bisect_left(c[i],j)] != j:
            print(mh+mw)
            exit()
print(mh+mw-1)

Solution (Python):
from bisect import bisect_left
import sys
input = sys.stdin.readline
H,W,m = map(int,input().split())
h = [0]*(H+1)
w = [0]*(W+1)
c = [[-1,10**6] for i in range(H+1)]
for i in range(m):
    a,b = map(int,input().split())
    h[a] += 1
    w[b] += 1
    c[a].append(b)
mh = max(h)
mw = max(w)
hkouho = []
wkouho = []
for i in range(H+1):
    if h[i] == mh:
        hkouho.append(i)
for i in range(W+1):
    if w[i] == mw:
        wkouho.append(i)
for i in hkouho:
    c[i].sort()
    for j in wkouho:
        if c[i][bisect_left(c[i],j)] != j:
            print(mh+mw)
            exit()
print(mh+mw-1)

Solution (Python):
h, w, m = map(int, input().split())
hw = []
h_cnt = [0] * h
w_cnt = [0] * w
hw = []
hw_set = set()
for _ in range(m):
    r, c = map(int, input().split())
    r -= 1
    c -= 1
    h_cnt[r] += 1
    w_cnt[c] += 1
    hw.append((r, c))
    hw_set.add((r, c))
mh = max(h_cnt)
mw = max(w_cnt)
cand_r = []
for i in range(h):
    if h_cnt[i] == mh:
        cand_r.append(i)
cand_c = []
for j in range(w):
    if w_cnt[j] == mw:
        cand_c.append(j)
ans = mh + mw
for i in cand_r:
    for j in cand_c:
        if not (i, j) in hw_set:
            print(ans)
            exit()
print(ans - 1)

Solution (Python):
H, W, M = map(int, input().split())
h = [0] * (H+1)
w = [0] * (W+1)
l = set()
for i in range(M):
  x, y = map(int, input().split())
  h[x] += 1
  w[y] += 1
  l.add((x, y))
  
c = max(h)
d = max(w)
a = [i for i, x in enumerate(h) if x == c]
b = [i for i, x in enumerate(w) if x == d]

flag = False
for s in a:
  for t in b:
    if (s, t) not in l:
      flag = True
      break
  if flag:
    break
ans = c+d
if not flag:
  ans -= 1
print(ans)

Solution (Python):
h,w,m = list(map(int,input().split()))

bombDict = dict()
bombDictH = dict()
bombDictW = dict()


for i in range(h+1):
    bombDict[i] = set()
    bombDictH[i] = 0

for i in range(w+1):
    bombDictW[i] = 0


for i in range(m):
    bombH,bombW = list(map(int,input().split()))
    bombDictH[bombH] += 1
    bombDictW[bombW] += 1
    bombDict[bombH].add(bombW)

maxH = max(bombDictH,key = bombDictH.get)
maxW = max(bombDictW,key = bombDictW.get)
maxHV = max(bombDictH.values())
maxWV = max(bombDictW.values())

hList = list(bombDictH.values())
wList = list(bombDictW.values())

maxHList = []
maxWList = []

if hList.count(maxHV) > 1:
    for i in range(h+1):
        if hList[i] == maxHV:
            maxHList.append(i)
else:
    maxHList.append(maxH)

if wList.count(maxWV) > 1:
    for i in range(w+1):
        if wList[i] == maxWV:
            maxWList.append(i)
else:
    maxWList.append(maxW)

ans = 0

for i in maxHList:
    for j in maxWList:
        if j in bombDict[i]:
            ans = max(ans,bombDictH[i] + bombDictW[j] - 1)
        else:
            ans = max(ans,bombDictH[i] + bombDictW[j])
            break

print(ans)

Solution (Python):

from bisect import bisect_left
import sys
input = sys.stdin.readline
H,W,m = map(int,input().split())
h = [0]*(H+1)
w = [0]*(W+1)
c = [[-1,10**6] for i in range(H+1)]
for i in range(m):
    a,b = map(int,input().split())
    h[a] += 1
    w[b] += 1
    c[a].append(b)
mh = max(h)
mw = max(w)
hkouho = []
wkouho = []
for i in range(H+1):
    if h[i] == mh:
        hkouho.append(i)
for i in range(W+1):
    if w[i] == mw:
        wkouho.append(i)
for i in range(H+1):
    c[i].sort()


for i in hkouho:
    for j in wkouho:
        
        if c[i][bisect_left(c[i],j)] != j:
            print(mh+mw)
            exit()
print(mh+mw-1)

Solution (Python):
from collections import deque

def argmax_poss(a):
    if len(a) == 0:
        return []
    all_ = [0]
    max_ = a[0]
    for i in range(1, len(a)):
        if a[i] > max_:
            all_ = [i]
            max_ = a[i]
        elif a[i] == max_:
            all_.append(i)
    return all_

h,w,m = map(int,input().split())
Ms = []

h_scores = [0 for i in range(h)]
w_scores = [0 for i in range(w)]

record = set()

for i in range(m):
  h,w = map(int,input().split())
  record.add((h-1,w-1))
  h_scores[h-1] += 1
  w_scores[w-1] += 1

max_h_poss = argmax_poss(h_scores)
max_w_poss = argmax_poss(w_scores)

out_pos_count = 0 

is_ok = False

for h in max_h_poss:
    for w in max_w_poss:
        if (h,w) not in record:
            is_ok = True
            break
        
if is_ok:
    print(max(h_scores) + max(w_scores))
else:
    print(max(h_scores) + max(w_scores)-1)

Solution (Python):
from collections import Counter
import sys
H, W, M = map(int, input().split())

h = [0] * M
w = [0] * M
for i in range(M):
    h[i], w[i] = map(int, input().split())


S = Counter(h)
T = Counter(w)

if (M == 1):
    print(1)

else:
    if (S.most_common()[0][1] > T.most_common()[0][1]):
        smc = S.most_common()[0][0]
        for i in range(M):
            if (h[i] == smc):
                w[i] = 'boom'

        w1 = [s for s in w if s != 'boom']
        T = Counter(w1)
        if (len(w1) == 0):
            print(M)
            sys.exit()
        tmc = T.most_common()[0][0]
        for i in range(len(w1)):
            if (w1[i] == tmc):
                w1[i] = 'boom' 

        w2 = [s for s in w1 if s != 'boom']
        print(M-len(w2))

    else:
        tmc = T.most_common()[0][0]
        for i in range(M):
            if (w[i] == tmc):
                h[i] = 'boom'

        h1 = [s for s in h if s != 'boom']
        S = Counter(h1)
        if (len(h1) == 0):
            print(M)
            sys.exit()
        smc = S.most_common()[0][0]
        for i in range(len(h1)):
            if (h1[i] == smc):
                h1[i] = 'boom' 

        h2 = [s for s in h1 if s != 'boom']
        print(M-len(h2))

Solution (Python):
import sys
from collections import defaultdict
input = sys.stdin.readline
h,w,m=map(int, input().split())
hd=[0 for i in range(h+1)]
wd=[0 for i in range(w+1)]
hw=defaultdict(int)
hmax=0
wmax=0
for i in range(m):
    h0,w0=map(int, input().split())
    hd[h0]+=1
    hmax=max(hmax,hd[h0])
    wd[w0]+=1
    wmax=max(wmax,wd[w0])
    hw[(h0,w0)]+=1

max_h_list=[]
max_w_list=[]
for k in range(h+1):
    if hd[k]==hmax:
        max_h_list.append(k)

for k in range(w+1):
    if wd[k]==wmax:
        max_w_list.append(k)

ans=float('inf')

for x in max_h_list:
    for y in max_w_list:
        if hw[(x,y)]==1:
            ans=min(ans,1)
        else:
            ans=min(ans,0)
            break
print(hmax+wmax-ans)

Solution (Python):

import collections as cl
import sys


def II():
    return int(sys.stdin.readline())


def MI():
    return map(int, sys.stdin.readline().split())


def LI():
    return list(map(int, sys.stdin.readline().split()))


def main():
    h, w, m = MI()
    targets = [[] for i in range(h)]
    tate = [[] for i in range(w)]
    tate_length = [0] * w
    original = []
    lengths = [0] * h
    for i in range(m):
        target = LI()
        original.append(target)
        targets[target[0] - 1].append(target[1] - 1)
        tate[target[1] - 1].append(target[0] - 1)
        lengths[target[0] - 1] += 1
        tate_length[target[1] - 1] += 1

    max_length = max(lengths)
    max_length_tate = max(tate_length)

    max_w_indexes = [i for i, x in enumerate(
        tate_length) if x == max_length_tate]

    max_h_indexes = [i for i, x in enumerate(
        lengths) if x == max_length]

    max_h_indexes = set(max_h_indexes)
    max_w_indexes = set(max_w_indexes)

    ttl = len(max_h_indexes) * len(max_w_indexes)

    for target in original:
        if target[0] - 1 in max_h_indexes and target[1] - 1 in max_w_indexes:
            ttl -= 1

    if ttl > 0:
        print(max_length + max_length_tate)
    else:
        print(max_length+max_length_tate - 1)


main()

Solution (Python):
def main():
    h, w, m = map(int, input().split())
    h_bomb_dict = {}
    w_bomb_dict = {}
    bombs = []
    for i in range(m):
        zh, zw = map(int, input().split())
        bombs.append((zh, zw))
        if zh in h_bomb_dict.keys():
            h_bomb_dict[zh] += 1
        else:
            h_bomb_dict[zh] = 1

        if zw in w_bomb_dict.keys():
            w_bomb_dict[zw] += 1
        else:
            w_bomb_dict[zw] = 1
    bombs = set(bombs)

    hbombs = max(h_bomb_dict.values())
    wbombs = max(w_bomb_dict.values())
    h_maxs = []
    w_maxs = []
    for key, v in h_bomb_dict.items():
        if v == hbombs:
            h_maxs.append(key)

    for key, v in w_bomb_dict.items():
        if v == wbombs:
            w_maxs.append(key)

    for h in h_maxs:
        for w in w_maxs:
            if not (h, w) in bombs:
                print(hbombs + wbombs)
                return
    print(hbombs + wbombs-1)
if __name__ == '__main__':
    main()

Solution (Python):
import sys
import itertools

input = sys.stdin.readline

def my_index_multi(l, x):
    return [k for k, _x in enumerate(l) if _x == x]

h,w,m = map(int,input().split())
l_h = [0]*(h+1)
l_w = [0]*(w+1)
l_b = set()

for _ in range(m):
    h,w = map(int,input().split())
    l_h[h] += 1
    l_w[w] += 1
    l_b.add((h,w))

m_h = max(l_h)
m_w = max(l_w)

l_h_2 = []
for i, x in enumerate(l_h):
    if x == m_h:
        l_h_2.append(i)

l_w_2 = []
for i, x in enumerate(l_w):
    if x == m_w:
        l_w_2.append(i)

ans = m_h + m_w

for i,j in itertools.product(l_h_2,l_w_2):
    if (i,j) not in l_b:
        break
else:
    ans -= 1

print(ans)

Solution (Python):
import glob
import os
import numpy as np

bn = os.path.basename(__file__).split('.')[0]
dn = os.path.dirname(__file__).split('/')


REL_PATH = dn[len(dn)-2] + '\\' + dn[len(dn)-1] + '\\' + bn


TOP_PATH = 'C:\\AtCoder'

class Common:
    problem = []
    index = 0

    def __init__(self, rel_path):
        self.rel_path = rel_path

    def initialize(self, path):
        file = open(path)
        self.problem = file.readlines()
        self.index = 0
        return

    def input_data(self):
        try:
            IS_TEST
            self.index += 1
            return self.problem[self.index - 1]

        except NameError:
            return input()

    def resolve(self):
        pass

    def exec_resolve(self):
        try:
            IS_TEST
            for path in glob.glob(TOP_PATH + '\\' + self.rel_path + '/*.txt'):
                print("Test: " + path)
                self.initialize(path)
                self.resolve()
                print("\n\n")
        except NameError:
            self.resolve()


class Solver(Common):

    def resolve(self):

        H, W, M = map(int, self.input_data().split())
        B = [None for i in range(M)]

        ver_num =[0 for i in range(W+1)] 
        hol_num = [0 for i in range(H+1)] 

        for i in range(M):
            B[i] = list(map(int, self.input_data().split()))
            ver_num[B[i][1]] +=1
            hol_num[B[i][0]] +=1

        ver_max = np.max(np.array(ver_num))
        hol_max = np.max(np.array(hol_num))

        max_columns = []
        max_rows = []

        for i in range(1,W+1):
            if ver_max == ver_num[i]:
                max_columns.append(i)
        for i in range(1,H+1):
            if hol_max == hol_num[i]:
                max_rows.append(i)

        b_cross = 0
        for b in B:
            if ver_num[b[1]] == ver_max and hol_num[b[0]] == hol_max:
                b_cross += 1
        if b_cross == len(max_columns) * len(max_rows):
            result = ver_max + hol_max - 1
        else:
            result = ver_max + hol_max
        print(str(result))

solver = Solver(REL_PATH)
solver.exec_resolve()

Solution (Python):
import sys;input=sys.stdin.readline
H, W, M = map(int, input().split())
dx = [0]*H
dy = [0]*W
HH = set()
for _ in range(M):
    x, y = map(int, input().split())
    dx[x-1] += 1
    dy[y-1] += 1
    HH.add((x-1, y-1))
mx=max(dx)
my=max(dy)
mxs = set()
mys = set()
for i in range(H):
    if dx[i] == mx:
        mxs.add(i)
for i in range(W):
    if dy[i] == my:
        mys.add(i)

for x in mxs:
    for y in mys:
        if (x, y) not in HH:

            print(mx+my)
            sys.exit()
print(mx+my-1)

Solution (Python):
from sys import exit, stdin


from collections import deque, Counter


input = stdin.readline

H, W, M = map(int, input().split())

col = Counter()
row = Counter()
D = Counter()
for i in range(M):
    h, w = input().split()
    row.update([h])
    col.update([w])
    D.update([h + w])

rtop = row.most_common(1)[0]
ctop = col.most_common(1)[0]


for c in col.most_common():
    if c[1] < ctop[1]:
        break
    else:
        if D[rtop[0] + c[0]] == 0:
            ans = rtop[1] + c[1]
            break
        else:
            ans = rtop[1] + c[1] - 1

for r in row.most_common():
    if r[1] < rtop[1]:
        break
    else:
        if D[r[0] + ctop[0]] == 0:
            ans2 = r[1] + ctop[1]
            break
        else:
            ans2 = r[1] + c[1] - 1

print(max(ans, ans2))

Solution (Python):
import sys
h,w,m = map(int, input().split())
h_t = [0 for _ in range(h)]
w_t = [0 for _ in range(w)]
t = []
for _ in range(m):
  hi,wi = map(int, input().split())
  h_t[hi-1] += 1
  w_t[wi-1] += 1
  t.append([hi-1,wi-1])
hmax = max(h_t)
wmax = max(w_t)
hmaxi = [i1 for i1 in range(h) if h_t[i1] == hmax]
wmaxi = [i2 for i2 in range(w) if w_t[i2] == wmax]
c = len(hmaxi)*len(wmaxi)
d = 0
for ht,wt in t:
  if h_t[ht] == hmax:
    if w_t[wt] == wmax:
      d += 1
if c ==d:
  print(hmax + wmax-1)
else:
  print(hmax + wmax)

Solution (Python):
import collections 

h,w,m=map(int,input().split())
x=[]
y=[]
t=[]

for _ in range(m):
  a=list(map(int,input().split()))
  x.append(a[0])
  y.append(a[1])
  t.append(a)
  
X=collections.Counter(x)
Y=collections.Counter(y)

va,co=zip(*Y.most_common())
va1,co1=zip(*X.most_common())
X1=co1[0]
Y1=co[0]
chx=0
chy=0

for i in va:
  if Y[i]==Y1:
    chy+=1
    
for j in va1:
  if X[j]==X1:
    chx+=1


ans=0
for r in t:
  h=r[0]
  g=r[1]
  if X[h]==co1[0] and Y[g]==co[0]:
    ans+=1
    
if ans<(chx*chy):
  print(X1+Y1)
  
else:
  print(X1+Y1-1)

Solution (Python):
h,w,m=map(int,input().split())
hh=[[0,i]for i in range(h)]
ww=[[0,i]for i in range(w)]
hw=set()
for _ in range(m):
  a,b=map(int,input().split())
  a-=1
  b-=1
  hh[a][0]+=1
  ww[b][0]+=1
  hw.add((a,b))
ww.sort(reverse=1)
s=ww[0][0]
w=[]
for x,j in ww:
  if x==s:w.append(j)
hh.sort(reverse=1)
ans=0
t=max(hh)[0]
for j in w:
  for x,i in hh:
    if x!=t:break
    if (i,j) in hw:
      ans=s+x-1
    else:
      exit(print(s+x))
print(ans)