#include <bits/stdc++.h>
#include "tickets.h"
#define all(x) (x).begin(),(x).end()
using namespace std;
using ll = long long;
using ld = long double;
//#define int ll
#define sz(x) ((int)(x).size())
using pii = pair<int,int>;
using tii = tuple<int,int,int>;
const int nmax = 1500 + 5;
void partition(int k, vector<vector<int>> wsign) {
int n = sz(wsign), m = sz(wsign[0]);
vector<pii> freq(n, pii{0, 0});
vector<deque<int>> sorted(n);
vector<vector<int>> rez(n, vector<int>(m, -1));
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) if(wsign[i][j] == -1) sorted[i].emplace_back(j), freq[i].first++;
for(int j = 0; j < m; j++) if(wsign[i][j] == 1) sorted[i].emplace_back(j), freq[i].second++;
}
for(int Q = 0; Q < k; Q++) {
vector<int> checked(n);
vector<int> atr(n);
iota(all(atr), 0);
sort(all(atr), [&](auto a, auto b) { return freq[a].first > freq[b].first; });
for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
int i = atr[T];
if(checked[i]) continue;
if(freq[i].first > 0) {
rez[i][sorted[i].front()] = Q;
sorted[i].pop_front();
cnt++;
checked[i] = 1;
freq[i].first--;
}
}
sort(all(atr), [&](auto a, auto b) { return freq[a].second > freq[b].second; });
for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
int i = atr[T];
if(checked[i]) continue;
if(freq[i].second > 0) {
rez[i][sorted[i].back()] = Q;
sorted[i].pop_back();
cnt++;
checked[i] = 1;
freq[i].second--;
}
}
}
allocate_tickets(rez);
return;
}
const ll infll = 1e18 + 5;
const int nnmax = 300 + 5;
ll S2(int k, vector<vector<int>> d) {
int n = sz(d), m = sz(d[0]);
vector<vector<ll>> dp(n + 1, vector<ll>(k * n / 2 + 2, -infll));
vector<vector<int>> with(n + 1, vector<int>(k * n / 2 + 2, 0));
reverse(all(d));
d.emplace_back(vector<int>());
reverse(all(d));
//for(int j = 1; j < sz(dp[0]); j++) dp[0][j] = -infll;
dp[0][0] = 0;
for(int i = 1; i <= n; i++) {
vector<int> tmp = d[i];
sort(all(tmp));
vector<ll> cost(k + 1);
ll tmpsum = 0;
for(int i = 0; i < k; i++) {
tmpsum += tmp[i];
cost[i + 1] -= tmpsum;
}
tmpsum = 0;
for(int i = 0, j = sz(tmp) - 1; i < k; i++, j--) {
tmpsum += tmp[j];
cost[k - i - 1] += tmpsum;
}
int lim = min(k * n / 2, i * k);
for(int j = 0; j <= lim; j++) {
int mnw = 0;
dp[i][j] = -infll;
for(int minus = 0; minus <= min(j, k); minus++) {
if(dp[i - 1][j - minus] + cost[minus] > dp[i][j]) {
mnw = minus;
dp[i][j] = dp[i - 1][j - minus] + cost[minus];
}
}
with[i][j] = mnw;
//cerr << dp[i][j] << ' ';
}
//cerr << '\n';
}
//cerr << "finished\n";
int current = n / 2 * k;
vector<vector<int>> wsign(n, vector<int>(m, 0));
for(int i = n; i > 0; i--) {
vector<int> atr(m);
iota(all(atr), 0);
sort(all(atr), [&](int a, int b) { return d[i][a] < d[i][b]; });
//cerr << sz(with[i]) << ' ' << current << '\n';
int u = with[i][current];
current -= u;
//cerr << u << '\n';
for(int j = 0; j < u; j++)
//cerr << atr[j] << '\n',
wsign[i - 1][atr[j]] = -1;
for(int j = m - 1, t = 0; t < k - u; t++, j--)
//cerr << atr[j] << '\n',
wsign[i - 1][atr[j]] = 1;
}
//cerr << current << '\n';
partition(k, wsign);
//cerr << "better\n";
ll sum = 0;
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++)
//cerr << wsign[i][j] << ' ',
sum += wsign[i][j] * d[i + 1][j];
//cerr << '\n';
}
return sum;
}
ll S3(int k, vector<vector<int>> d) {
int n = sz(d), m = sz(d[0]);
vector<pii> freq(n, pii{0, 0});
vector<deque<int>> sorted(n);
vector<vector<int>> rez(n, vector<int>(m, -1));
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) if(d[i][j] == 0) sorted[i].emplace_back(j), freq[i].first++;
for(int j = 0; j < m; j++) if(d[i][j] == 1) sorted[i].emplace_back(j), freq[i].second++;
}
ll sum = 0;
for(int Q = 0; Q < k; Q++) {
vector<int> checked(n);
vector<int> atr(n);
iota(all(atr), 0);
sort(all(atr), [&](auto a, auto b) { return freq[a].first > freq[b].first; });
int total = 0;
for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
int i = atr[T];
if(checked[i]) continue;
if(freq[i].first > 0) {
rez[i][sorted[i].front()] = Q;
sorted[i].pop_front();
cnt++;
checked[i] = 1;
freq[i].first--;
}
}
sort(all(atr), [&](auto a, auto b) { return freq[a].second > freq[b].second; });
for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
int i = atr[T];
if(checked[i]) continue;
if(freq[i].second > 0) {
total++;
rez[i][sorted[i].back()] = Q;
sorted[i].pop_back();
cnt++;
checked[i] = 1;
freq[i].second--;
}
}
for(int T = 0; T < n; T++) {
int i = atr[T];
if(checked[i]) continue;
if(freq[i].second > 0)
total++,
freq[i].second--;
else
freq[i].first--;
rez[i][sorted[i].back()] = Q;
sorted[i].pop_back();
checked[i] = 1;
}
sum += min(total, n - total);
}
allocate_tickets(rez);
return sum;
}
ll S4(int k, vector<vector<int>> d) {
vector<pii> values;
int n = sz(d), m = sz(d[0]);
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
values.emplace_back(i, j);
sort(all(values), [&](auto a, auto b) { return d[a.first][a.second] < d[b.first][b.second]; });
vector<vector<int>> signs(n, vector<int>(m, 1));
for(int i = 0; i < n / 2 * k; i++)
signs[values[i].first][values[i].second] = -1;
partition(k, signs);
ll sum = 0;
for(auto [a, b] : values) {
sum += d[a][b] * signs[a][b];
}
return sum;
}
ll S1(int k, vector<vector<int>> d) {
int n = sz(d), m = 1;
vector<vector<int>> rez(n, vector<int>(m, 0));
allocate_tickets(rez);
vector<int> v;
for(auto a : d)
for(auto x : a) v.emplace_back(x);
sort(all(v));
ll sum = 0;
for(int i = 0; i < n; i++)
sum += v[i];
for(int i = 0; i < n / 2; i++)
sum -= 2 * v[i];
return sum;
}
long long find_maximum(int k, std::vector<std::vector<int>> d) {
bool ok = 1;
for(auto a : d)
for(auto x : a)
ok &= (x == 0 || x == 1);
if(ok)
return S3(k, d);
else if(sz(d[0]) == 1) return S1(k, d);
else if(k == sz(d[0]))
return S4(k, d);
else
return S2(k, d);
}
/**
Anul asta se da centroid.
-- Surse oficiale
*/
