#include "tickets.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define sig signed
#define arr array
#define vec vector
#define pii pair<int, int>
#define fir first
#define sec second
#define mp make_pair
const int N = 1505, M = 1505, INF = 1e18;
int n, m, k;
arr<arr<int, M>, N> a, b;
arr<int, N> lst, mst;
void prp_cmp() {
for (int i = 1; i <= n; i++) {
lst[i] = INF, mst[i] = -1;
for (int j = 1; j <= m; j++)
if (!b[i][j]) lst[i] = min(lst[i], a[i][j]), mst[i] = max(mst[i], a[i][j]);
// cout << i << ": " << lst[i] << " " << mst[i] << '\n';
}
}
arr<arr<pii, N>, N> dp;
void dp_cmp() {
dp[0].fill({-INF, -1});
dp[0][0] = {0, -1};
for (int i = 1; i <= n; i++) {
for (int c = 0; c <= n / 2; c++) {
int tk = (c == 0) ? -INF : dp[i - 1][c - 1].fir + mst[i];
int lv = dp[i - 1][c].fir - lst[i];
dp[i][c] = max(mp(tk, 1), mp(lv, 0));
}
}
}
arr<int, N> dr;
void dr_cmp() {
int i = n, c = n / 2;
while (i != 0) {
dr[i] = dp[i][c].sec;
if (dr[i] == 0) i--;
else i--, c--;
}
}
void upd(int x) {
for (int i = 1; i <= n; i++) {
int mn = -1, mx = -1;
for (int j = 1; j <= m; j++) {
if (b[i][j]) continue;
if (a[i][j] == lst[i]) mn = j;
if (a[i][j] == mst[i]) mx = j;
}
if (dr[i] == 0) b[i][mn] = x;
else b[i][mx] = x;
}
}
// Return indices 0-indexed
int find_maximum(sig _k, vec<vec<sig>> _a) {
n = _a.size(), m = _a[0].size(), k = _k;
for (int i = 1; i <= n; i++)
for (int j = 1; j <= m; j++)
a[i][j] = _a[i - 1][j - 1];
int ans = 0;
for (int x = 1; x <= k; x++) {
prp_cmp();
dp_cmp();
dr_cmp();
upd(x);
ans += dp[n][n / 2].fir;
}
vec<vec<sig>> ass;
for (int i = 1; i <= n; i++) {
vec<sig> x;
for (int j = 1; j <= m; j++) x.push_back(b[i][j] - 1);
ass.push_back(x);
}
allocate_tickets(ass);
return ans;
}
