#include "tickets.h"
#include "bits/stdc++.h"
using namespace std;
#define FAST ios_base::sync_with_stdio(false); cin.tie(0);
#define pb push_back
#define eb emplace_back
#define ins insert
#define f first
#define s second
#define cbr cerr<<"hi\n"
#define mmst(x, v) memset((x), v, sizeof ((x)))
#define siz(x) ll(x.size())
#define all(x) (x).begin(), (x).end()
#define lbd(x,y) (lower_bound(all(x),y)-x.begin())
#define ubd(x,y) (upper_bound(all(x),y)-x.begin())
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); //can be used by calling rng() or shuffle(A, A+n, rng)
inline long long rand(long long x, long long y) { return rng() % (y+1-x) + x; } //inclusivesss
string inline to_string(char c) {string s(1,c);return s;} template<typename T> inline T gcd(T a,T b){ return a==0?llabs(b):gcd(b%a,a); }
using ll=long long;
using ld=long double;
#define FOR(i,s,e) for(ll i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
using pi=pair<ll,ll>; using spi=pair<ll,pi>; using dpi=pair<pi,pi>;
long long LLINF = 1e18;
int INF = 1e9+1e6;
#define MAXN (200006)
int n, m;
ll ans;
long long find_maximum(int k, std::vector<std::vector<int>> x) {
n = x.size(), m = x[0].size(), ans = 0;
vector<vector<int>> ret(n, vector<int>(m, -1));
vector<int> front(n, 0), back(n, m-1);
FOR(K,0,k-1) {
vector<spi> v;
vector<int> f(n, 1), out(n, -1);
multiset<pi,greater<pi>> ms;
ll mx = -LLINF, sum = 0, fc = 0, bc = 0, mid=0;
FOR(i,0,n-1) {
v.eb(x[i][front[i]], pi(i, 0)), v.eb(x[i][back[i]], pi(i, 1));
sum += x[i][back[i]] - ll(1e9), ++ bc;
}
sort(all(v));
for(auto i:v) {
int ind = i.s.f;
if(i.s.s == 1) { // is a .back()
ms.erase(pi(-x[ind][front[ind]] - (x[ind][back[ind]] - ll(1e9)), ind));
++ fc, sum -= x[ind][back[ind]] - ll(1e9), sum += -x[ind][front[ind]], mid = max(mid, (ll)x[ind][front[ind]]);
f[ind] = 0;
} else {
ms.ins(pi(-x[ind][front[ind]] - (x[ind][back[ind]] - ll(1e9)), ind));
-- bc;
f[ind] = -1;
}
if(fc > n/2) break;
if(bc > n/2) continue;
// check if optimum
vector<bool> ft(n, 1);
FOR(i,0,n-1) if(f[i] != -1) ft[i]=f[i]; else f[i]=1;
ll tmp=mid * (n/2-1) + (ll(1e9) - mid) * (n/2);
auto itr = ms.begin();
FOR(ii,1,n/2 - fc) { // change to front
assert(itr!=ms.end()), tmp += itr->f, ft[itr->s]=0, ++ itr;
}
if(sum + tmp > mx) {
mx = sum + tmp;
FOR(i,0,n-1) {
out[i] = ft[i];
}
}
}
assert(count(all(out), 0) == n/2 && count(all(out), 1) == n/2);
ans += mx;
FOR(i,0,n-1) {
if(out[i]) {
ret[i][back[i]]=K, -- back[i];
} else {
ret[i][front[i]]=K, ++front[i];
}
}
}
allocate_tickets(ret);
return ans;
}
