#include "tickets.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll MOD = 998244353;
const ll INF = 1e18;
const ld EPS = 1e-12;
#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);
ll find_maximum(int k, vector<vector<int>> x) {
ll n = x.size();
ll m = x[0].size();
ll ans = 0;
// sort by val, keep track of pos
vector<vector<int>> pos(n, vector<int>(m));
REP(i, 0, n) {
REP(j, 0, m) {
pos[i][j] = j;
}
sort(all(pos[i]), [&](const int &a, const int &b) -> bool {
return x[i][a] < x[i][b];
});
}
auto find = [&](const int &i, const int &j) {
return x[i][pos[i][j]];
};
// [val, color]
priority_queue<pair<int, int>> pq;
// track max's and min's
vector<int> add(n, 0), sub(n, 0);
// b will always be median
// ans will always be greatest n/2 minus smallest n/2
REP(i, 0, n) {
// take smallest k
REP(j, 0, k) {
ans -= find(i, j);
}
pq.push({find(i, m-1) + find(i, k-1), i});
}
// take greatest n/2 paired with its smallest to balance sum properly
REP(i, 0, n * k / 2) {
pair<int, int> cand = pq.top(); pq.pop();
ans += cand.first;
// cap is at k tickets per color
add[cand.second]++;
if (add[cand.second] < k) {
pq.push({find(cand.second, m-1-add[cand.second]) + find(cand.second, k-1-add[cand.second]), cand.second});
}
}
priority_queue<pair<int, int>>().swap(pq);
vector<vector<int>> g(n, vector<int>(m, -1));
vector<bool> use(n, false);
// [cnt, color]
REP(i, 0, n) {
pq.push({add[i], i});
}
// apply
// REP(i, 0, k) {
// fill(all(use), false);
// // n/2 colors take max, n/2 colors take min
// REP(j, 0, n / 2) {
// pair<int, int> cand = pq.top(); pq.pop();
// use[cand.second] = true;
// }
// REP(j, 0, n) {
// if (use[j]) {
// g[j][pos[j][m-add[j]]] = i;
// add[j]--;
// pq.push({add[j], j});
// } else {
// g[j][pos[j][sub[j]]] = i;
// sub[j]++;
// }
// }
// }
allocate_tickets(g);
return ans;
}
