#include <algorithm>
#include <iostream>
#include <fstream>
#include <climits>
#include <cmath>
#include <vector>
#include <stack>
#include <iomanip>
#include <queue>
// #include <bits/std++.h>
#define in fin
#define out fout
using namespace std;
const int NMAX = 400 * 2 + 5;
const float eps = 1e-5;
ifstream fin("adapost.in");
ofstream fout("adapost.out");
struct muchie{
int x, y, pereche, c, f;
float cost;
};
struct punct{
float x, y;
};
float distanta(punct &a, punct &b){
return sqrt( (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y) );
}
vector<muchie> mch;
vector<int> g[NMAX];
int sursie, noelle;
int cuplaj[NMAX];
bool mrc[NMAX];
int n;
float unchii[NMAX], perchance[NMAX], the_real_ones[NMAX];
pair<int, int> last[NMAX];
void add_muchie(int x, int y, int c, float cost){
int id = mch.size(), idp = mch.size() + 1;
mch.push_back({x, y, idp, c, 0, cost});
mch.push_back({y, x, id, 0, 0, -cost});
g[x].push_back(id);
g[y].push_back(idp);
}
bool pair_up(int nod, float dist){
if(mrc[nod]) return 0;
mrc[nod] = 1;
// cerr << "dist = " << dist << '\n';
for(const int &id : g[nod]){
int cop = mch[id].y;
if(mch[id].cost > dist) continue;
if(-mch[id].cost > dist) continue;
if(cop == sursie || cop == noelle) continue; // ei nu conteaza la cuplaj
// cerr << "cuplaj[cop] = " << cuplaj[cop] << '\n';
if(!cuplaj[cop] || pair_up(cuplaj[cop], dist)){
cuplaj[cop] = nod;
cuplaj[nod] = cop;
// cerr << "--> fac pair up" << '\n';
return 1;
}
}
return 0;
}
bool verifica_te_rog(float dist){
for(int i = 1; i <= 2 * n + 2; i++){
cuplaj[i] = 0;
}
int total = 0;
// cerr << "incep sa verific dist = " << fixed << setprecision(3) << dist << '\n';
bool ghost_bath_is_asa_peak = 1; // in special albumui burial
while(ghost_bath_is_asa_peak){ // asta e ca un while true cu conditia asta...
ghost_bath_is_asa_peak = 0;
for(int i = 1; i <= n; i++) mrc[i] = 0;
for(int i = 1; i <= n; i++){
// cerr << "i = " << i << '\n';
if(!cuplaj[i] && pair_up(i, dist)){
ghost_bath_is_asa_peak = 1;
total++;
// cerr << "adaug unu pentru i = " << i << '\n';
}
}
}
// cerr << "total = " << total << '\n';
return (total == n); // toti gasesc adapost in dist rezonabila
}
// ew flux
void clopot_barbat_vad(){
for(int i = 1; i <= 2 * n + 2; i++){
unchii[i] = INT_MAX;
mrc[i] = 0;
}
queue<int> q;
q.push(sursie);
unchii[sursie] = 0;
mrc[sursie] = 1;
while(!q.empty()){
int x = q.front(); q.pop();
for(const int &id : g[x]){
int y = mch[id].y;
if(unchii[y] > unchii[x] + mch[id].cost && mch[id].c > mch[id].f){
unchii[y] = unchii[x] + mch[id].cost;
if(!mrc[y]){
q.push(y);
mrc[y] = 1;
}
}
}
mrc[x] = 0;
}
}
float cost = 0, flux = 0;
float maxim_ude = 0;
bool deschistra(){
for(int i = 1; i <= 2 * n + 2; i++){
perchance[i] = INT_MAX;
last[i] = {0, -1};
}
priority_queue< pair<float, int>, vector< pair<float, int> >, greater< pair<float, int> > > pq;
perchance[sursie] = 0;
the_real_ones[sursie] = 0;
pq.push({0, sursie});
while(!pq.empty()){
int x = pq.top().second;
float d = pq.top().first;
pq.pop();
// cerr << "x initial = " << x << " d = " << d << '\n';
if(d != perchance[x]) continue;
// benighted
// cerr << "x = " << x << '\n';
for(const int &id : g[x]){
int y = mch[id].y;
if(mch[id].c == mch[id].f) continue;
if(mch[id].cost > maxim_ude) continue;
if(-mch[id].cost > maxim_ude) continue;
// cerr << "--> y = " << y << '\n';
float im_a_new_soul = perchance[x] + mch[id].cost + unchii[x] - unchii[y];
// cerr << "--> new = " << im_a_new_soul << " per = " << perchance[y] << '\n';
if(im_a_new_soul < perchance[y]){
// cerr << "----> sa stii ca am chiar intrat\n";
perchance[y] = im_a_new_soul;
the_real_ones[y] = the_real_ones[x] + mch[id].cost;
pq.push({perchance[y], y});
last[y] = {x, id};
// im a new soul, i came to this strange world
// hoping i could learn a bit 'bout how to give and take
// but since i came here
// felt the joy and the fear
// finding myself making every posible mistake
}
}
}
// cerr << "am iesit cu bile\n";
for(int i = 1; i <= 2 * n + 2; i++){
unchii[i] = the_real_ones[i];
}
// cerr << "perchance = " << perchance[noelle] << '\n';
if(perchance[noelle] == INT_MAX){
return 0;
}
// gasesc pathul
int minim_ude = INT_MAX;
int nod = noelle;
float sum = 0;
while(nod != sursie){
// cerr << "nod = " << nod << '\n';
int id = last[nod].second;
// sum += mch[id].cost;
minim_ude = min(minim_ude, mch[id].c - mch[id].f);
nod = last[nod].first;
}
// cerr << "minim_ude = " << minim_ude << '\n';
// cerr << "perchance[noelle] = " << perchance[noelle] << " last = " << last[noelle].first << '\n';
// cerr << "sum = " << sum << " real = " << the_real_ones[noelle] << '\n';
flux += minim_ude;
cost += (float)minim_ude * the_real_ones[noelle];
nod = noelle;
while(nod != sursie){
int id = last[nod].second;
mch[id].f += minim_ude;
mch[ mch[id].pereche ].f -= minim_ude;
nod = last[nod].first;
}
return 1;
}
void fa_flux_te_ROG(){
// clopot_barbat_vad();
// cerr << "Dupa clopotul\n";
while(deschistra());
}
signed main(){
ios_base::sync_with_stdio(false);
in.tie(NULL);
in >> n;
punct sold[n], adp[n];
for(int i = 0; i < n; i++) in >> sold[i].x >> sold[i].y;
for(int i = 0; i < n; i++) in >> adp[i].x >> adp[i].y;
sursie = 2 * n + 1;
noelle = sursie + 1;
for(int i = 0; i < n; i++){
for(int j = 0; j < n; j++){
// cout << "i = " << i << " j = " << j << " dist = " << distanta(sold[i], adp[j]) << '\n';
add_muchie(i + 1, j + n + 1, 1, distanta(sold[i], adp[j]));
}
}
float l = 0, r = 10000.0;
float sol = 0;
for(int it = 0; it < 25; it++){
float m = (l + r) / 2.0;
if(verifica_te_rog(m)){
sol = m;
r = m - eps;
}else l = m + eps;
}
out << fixed << setprecision(4) << sol << " ";
maxim_ude = sol;
// cerr << "sursie = " << sursie << " noelle = " << noelle << '\n';
for(int i = 1; i <= n; i++){
add_muchie(sursie, i, 1, 0);
add_muchie(i + n, noelle, 1, 0);
}
// cerr << "am ajuns aici\n";
// ew flux
fa_flux_te_ROG();
out << cost << '\n';
// out << "flux = " << flux << '\n';
return 0;
}