#include "tickets.h"
#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef pair<int,int> pi;
typedef vector<pi> pii;
typedef tuple<int,int,int> ti;
typedef vector<ll> li;
typedef vector<li> lii;
 
#define REP(i,a,b) for(int i=a;i<b;i++)
#define F first
#define S second
#define PB push_back
#define LSOne(s) ((s)&(-s))
#define all(x) x.begin(),x.end()
 
ll INF=1000000000000000010;
int inf=1e9+10;
ll M=1e9+7;
ll dp[1500][1500];
long long find_maximum(int x, std::vector<std::vector<int>> X) {
	int n = X.size();
	int m = X[0].size();
	vii a(n,vi(m,-1));
	int k=n/2;
	vector<pair<ll,ll>> b(n,{INF,-INF});
	REP(i,0,n)REP(j,0,m)b[i]={min(b[i].F,(ll)X[i][j]),max(b[i].S,(ll)X[i][j])};
	dp[0][0]=-b[0].F;
	dp[0][1]=b[0].S;
	REP(i,1,n)REP(j,0,k+1){
		dp[i][j]=dp[i-1][j]-b[i].F;
		if(j!=0)dp[i][j]=max(dp[i][j],dp[i-1][j-1]+b[i].S);
	}
	pi pos={n-1,k};
	vi arr(n,0);
	while(pos.F!=0){
		auto [x,y]=pos;
		if(dp[x][y]==dp[x-1][y]-b[x].F){
			arr[x]=1;
			pos={x-1,y};
		}
		else pos={x-1,y-1};
	}
	if(pos.S==0)arr[0]=1;
	REP(i,0,n){
		if(arr[i])REP(j,0,n){
			if(b[i].F==X[i][j]){
				a[i][j]=0;
				break;
			}
		}
		else REP(j,0,n){
			if(b[i].S==X[i][j]){
				a[i][j]=0;
				break;
			}
		}
	}
	allocate_tickets(a);
	return dp[n-1][k];
}
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