#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(long long i=0;i<(long long)(n);i++)
#define REP(i,k,n) for(long long i=k;i<(long long)(n);i++)
#define all(a) a.begin(),a.end()
#define pb emplace_back
#define eb emplace_back
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
#define ub(v,k) (upper_bound(all(v),k)-v.begin())
#define fi first
#define se second
#define pi M_PI
#define PQ(T) priority_queue<T>
#define SPQ(T) priority_queue<T,vector<T>,greater<T>>
#define dame(a) {out(a);return 0;}
#define decimal cout<<fixed<<setprecision(15);
#define dupli(a) {sort(all(a));a.erase(unique(all(a)),a.end());}
typedef long long ll;
typedef pair<ll,ll> P;
typedef tuple<ll,ll,ll> PP;
typedef tuple<ll,ll,ll,ll> PPP;
typedef multiset<ll> S;
using vi=vector<ll>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vvvvi=vector<vvvi>;
using vp=vector<P>;
using vvp=vector<vp>;
using vb=vector<bool>;
using vvb=vector<vb>;
const ll inf=1001001001001001001;
const ll INF=1001001001;
const ll mod=1000000007;
const double eps=1e-10;
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<'\n';}
template<class T> void outp(T a){cout<<'('<<a.fi<<','<<a.se<<')'<<'\n';}
template<class T> void outvp(T v){rep(i,v.size())cout<<'('<<v[i].fi<<','<<v[i].se<<')';cout<<'\n';}
template<class T> void outvvp(T v){rep(i,v.size())outvp(v[i]);}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<'\n';}
template<class T> void outvv(T v){rep(i,v.size())outv(v[i]);}
template<class T> bool isin(T x,T l,T r){return (l)<=(x)&&(x)<=(r);}
template<class T> void yesno(T b){if(b)out("yes");else out("no");}
template<class T> void YesNo(T b){if(b)out("Yes");else out("No");}
template<class T> void YESNO(T b){if(b)out("YES");else out("NO");}
template<class T> void noyes(T b){if(b)out("no");else out("yes");}
template<class T> void NoYes(T b){if(b)out("No");else out("Yes");}
template<class T> void NOYES(T b){if(b)out("NO");else out("YES");}
void outs(ll a,ll b){if(a>=inf-100)out(b);else out(a);}
ll gcd(ll a,ll b){if(b==0)return a;return gcd(b,a%b);}
ll modpow(ll a,ll b){ll res=1;a%=mod;while(b){if(b&1)res=res*a%mod;a=a*a%mod;b>>=1;}return res;}
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include "tickets.h"
vector<vector<int>> res;
void solve(int k){
ll n=res.size(),m=res[0].size();
vp t(n,P(0,k-1));
vvi id(n);
rep(i,n)rep(j,m)if(res[i][j]!=-1)id[i].pb(j);
rep(i,k){
ll zero=0,one=0;
rep(j,n)if(res[j][id[j][t[j].fi]]==1)one++;
rep(j,n){
if(res[j][id[j][t[j].se]]==0||one==n/2){
res[j][id[j][t[j].fi++]]=i;
}
else{
if(res[j][id[j][t[j].fi]]==0)one++;
res[j][id[j][t[j].se--]]=i;
}
}
}
}
long long find_maximum(int k, std::vector<std::vector<int>> x) {
ll n = x.size();
int m = x[0].size();
res=vector<vector<int>>(n,vector<int>(m,-1));
ll ans=0;
if(n<=300&&m<=300){
vvi rui(n,vi(k+1));
ll N=1;
while(N<n)N*=2;
rep(i,n){
rep(j,k)rui[i][0]+=x[i][m-j-1];
rep(j,k)rui[i][j+1]=rui[i][j]-x[i][j]-x[i][m-k+j];
}
vector<vector<PP>> seg(N+n-1);
rep(i,n)rep(j,k+1)seg[i+N-1].pb(rui[i][j],j,0);
for(int i=N-2;i>=0;i--){
if(i*2+2>n+N-1){
seg[i].pb(-INF,0,0);
continue;
}
if(i*2+2==n+N-1){
seg[i]=seg[i*2+1];continue;
}
rep(j,min((ll)(seg[i*2+1].size()+seg[i*2+2].size()-1),k*n/2+1))seg[i].pb(-inf,0,0);
rep(t,seg[i*2+1].size()){
rep(j,seg[i*2+2].size()){
if(t+j>k*n/2)break;
chmax(seg[i][t+j],PP(get<0>(seg[i*2+1][t])+get<0>(seg[i*2+2][j]),t,j));
}
}
}
ans=get<0>(seg[0][k*n/2]);
vi memo(2*N-1);
memo[0]=k*n/2;
rep(i,N-1){
if(i*2+1<N+n-1)memo[i*2+1]=get<1>(seg[i][memo[i]]);
if(i*2+2<N+n-1)memo[i*2+2]=get<2>(seg[i][memo[i]]);
}
rep(i,n){
rep(t,memo[i+N-1])res[i][t]=0;
rep(t,k-memo[i+N-1])res[i][m-t-1]=1;
}
solve(k);
}
else if(k==m){
vector<PP> v;
rep(i,n)rep(j,m)v.pb(x[i][j],i,j);
sort(all(v));
rep(t,n*m){
ll i,j,a;tie(a,i,j)=v[t];
if(t<n*m/2){
ans-=a;
res[i][j]=0;
}
else{
ans+=a;
res[i][j]=1;
}
}
solve(k);
}
else if(k==1){
vvp dp(n/2+1,vp(n/2+1,P(-inf,0)));
dp[0][0]=P(0,0);
rep(i,n/2+1)rep(j,n/2+1){
if(i!=n/2)chmax(dp[i+1][j],P(dp[i][j].fi-x[i+j][0],1));
if(j!=n/2)chmax(dp[i][j+1],P(dp[i][j].fi+x[i+j][m-1],0));
}
ans=dp[n/2][n/2].fi;
ll i=n/2,j=n/2;
while(i+j){
if(dp[i][j].se){
i--;
res[i+j][0]++;
}
else{
j--;
res[i+j][m-1]++;
}
}
}
else{
vi num(n,m);
rep(i,n)rep(j,m)if(x[i][j]==1)chmin(num[i],j);
vp t(n,P(0,m-1));
rep(i,k){
vp s(n);
ll zero=0,one=0;
rep(j,n)if(x[j][t[j].fi])one++;
rep(j,n)if(!x[j][t[j].se])zero++;
if(one>n/2){
ans+=n-one;
rep(j,n){
if(x[j][t[j].fi])res[j][t[j].se--]=i;
else{
res[j][t[j].fi++]=i;
num[j]--;
}
}
}
else if(zero>n/2){
ans+=n-zero;
rep(j,n){
if(!x[j][t[j].se]){
res[j][t[j].fi++]=i;
num[j]--;
}
else res[j][t[j].se--]=i;
}
}
else{
ans+=n/2;
vp s(n);
rep(j,n)s[j]=P(num[j],j);
sort(all(s));
rep(j,n){
if(x[s[j].se][t[s[j].se].se]==0||one==n/2){
res[s[j].se][t[s[j].se].fi++]=i;
num[s[j].se]--;
}
else{
if(x[s[j].se][t[s[j].se].fi]==0)one++;
res[s[j].se][t[s[j].se].se--]=i;
}
}
}
}
}
allocate_tickets(res);
return ans;
}
