#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
int INF = 10000000;
class TwinTowns
{
public:
vector <int> optimalTwinTowns(vector <int> x, vector <int> y, int maxPartners, int minDistance)
{
int N = x.size();
int cost[10][10];
for(int i=0; i<N; ++i)
for(int j=0; j<N; ++j)
{
int d = abs(x[i]-x[j]) + abs(y[i]-y[j]);
cost[i][j] = (d < minDistance ? INF : d);
}
vector<int> v(N, maxPartners);
pair<int,int> r = rec(0, N, v, cost);
vector<int> ans(2);
ans[0] = -r.first;
ans[1] = r.second;
return ans;
}
map< vector<int>,pair<int,int> > memo;
pair<int,int> rec(int i, int N, vector<int>& v, int cost[10][10])
{
if( i==N )
return make_pair(0, 0);
vector<int> key(v.begin()+i, v.end());
if( memo.count(key) )
return memo[key];
// choose at most v[i] js s.t. cost[i][j]!=INF && v[j]!=0
pair<int,int> best = rec(i+1, N, v, cost);
if( v[i] >= 1 )
{
for(int j1= i+1; j1<N; ++j1) if(cost[i][j1]!=INF && v[j1])
{
v[j1]--;
pair<int,int> a = rec(i+1, N, v, cost);
a.first -= 1;
a.second += cost[i][j1];
best = min(best, a);
v[j1]++;
}
}
if( v[i] >= 2 )
{
for(int j1= i+1; j1<N; ++j1) if(cost[i][j1]!=INF && v[j1])
for(int j2=j1+1; j2<N; ++j2) if(cost[i][j2]!=INF && v[j2])
{
v[j1]--;
v[j2]--;
pair<int,int> a = rec(i+1, N, v, cost);
a.first -= 2;
a.second += cost[i][j1] + cost[i][j2];
best = min(best, a);
v[j1]++;
v[j2]++;
}
}
if( v[i] >= 3 )
{
for(int j1= i+1; j1<N; ++j1) if(cost[i][j1]!=INF && v[j1])
for(int j2=j1+1; j2<N; ++j2) if(cost[i][j2]!=INF && v[j2])
for(int j3=j2+1; j3<N; ++j3) if(cost[i][j3]!=INF && v[j3])
{
v[j1]--;
v[j2]--;
v[j3]--;
pair<int,int> a = rec(i+1, N, v, cost);
a.first -= 3;
a.second += cost[i][j1] + cost[i][j2] + cost[i][j3];
best = min(best, a);
v[j1]++;
v[j2]++;
v[j3]++;
}
}
return memo[key] = best;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time;string timer() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
int verify_case(const vector <int> &Expected, const vector <int> &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: " << print_array(Expected) << endl; cerr << "\tReceived: " << print_array(Received) << endl; } return 0;}
template<int N> struct Case_ { Case_(){start_time=clock();} };
char Test_(...);
int Test_(Case_<0>) {
int x_[] = {0,0,10};
vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
int y_[] = {0,10,4};
vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
int maxPartners = 1;
int minDistance = 1;
int RetVal_[] = {1, 10 };
vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
int Test_(Case_<1>) {
int x_[] = {0,0,10};
vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
int y_[] = {0,10,4};
vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
int maxPartners = 1;
int minDistance = 11;
int RetVal_[] = {1, 14 };
vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
int Test_(Case_<2>) {
int x_[] = {0,10,0,10};
vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
int y_[] = {0,0,20,20};
vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
int maxPartners = 1;
int minDistance = 1;
int RetVal_[] = {2, 20 };
vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
int Test_(Case_<3>) {
int x_[] = {0,10,0,10};
vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
int y_[] = {0,0,20,20};
vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
int maxPartners = 2;
int minDistance = 10;
int RetVal_[] = {4, 60 };
vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
int Test_(Case_<4>) {
int x_[] = {0,0,0,0,0,0,0,0,0};
vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
int y_[] = {1,2,3,4,5,6,7,8,9};
vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
int maxPartners = 3;
int minDistance = 6;
int RetVal_[] = {6, 40 };
vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
template<> void Run_<-1>() {}
int main() { Run_<0>(); }
// END CUT HERE