Problem: A root tree is a directed acyclic graph that contains one node (root), from which there is exactly one path to any other node.

A root tree is binary if each node has at most two outgoing arcs.

When a binary tree is painted on the plane, all arcs should be directed from top to bottom. That is, each arc going from u to v must meet the condition yu > yv.

You've been given the coordinates of all tree nodes. Your task is to connect these nodes by arcs so as to get the binary root tree and make the total length of the arcs minimum. All arcs of the built tree must be directed from top to bottom.

Input

The first line contains a single integer n (2 ≤ n ≤ 400) — the number of nodes in the tree. Then follow n lines, two integers per line: xi, yi (|xi|, |yi| ≤ 103) — coordinates of the nodes. It is guaranteed that all points are distinct.

Output

If it is impossible to build a binary root tree on the given points, print "-1". Otherwise, print a single real number — the total length of the arcs in the minimum binary tree. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6. 

Examples

Input

3
0 0
1 0
2 1


Output

3.650281539872885


Input

4
0 0
1 0
2 1
2 0


Output

-1

Solution (in CPP):

Solution:
/*
 * Package: StandardCodeLibrary.Core
 * */
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <utility>
#include <vector>
#include <list>
#include <string>
#include <stack>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <numeric>
#include <bitset>
#include <complex>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <climits>
#if __GNUC__>=4 and __GNUC_MINOR__>=6
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
#endif
#ifdef  __GXX_EXPERIMENTAL_CXX0X__
#define typeof decltype
#endif
using namespace std;

#define lp for(;;)
#define repf(i,a,b) for (int i=(a);i<(b);++i)
#define rep(i,n) repf(i,0,n)
#define ft(i,a,b) for (int i=(a);i<=(b);++i)
#define fdt(i,a,b) for (int i=(a);i>=b;--i)
#define feach(e,s) for (typeof((s).begin()) e=(s).begin();e!=(s).end();++e)
#define fsubset(subset,set) for (int subset=(set)&((set)-1);subset;subset=(subset-1)&(set))
#define forin(i,charset) for (cstr i=(charset);*i;i++)
#define whl while
#define rtn return
#define fl(x,y) memset((x),char(y),sizeof(x))
#define clr(x) fl(x,char(0))
#define cpy(x,y) memcpy(x,y,sizeof(x))
#define pb push_back
#define mp make_pair
#define ins insert
#define ers erase
#define lb lower_bound
#define ub upper_bound
#define rnk order_of_key
#define sel find_by_order
#define x first
#define y second
#define sz(x) (int((x).size()))
#define all(x) (x).begin(),(x).end()
#define srt(x) sort(all(x))
#define uniq(x) srt(x),(x).erase(unique(all(x)),(x).end())
#define vec vector
#define pr pair
#define que queue
#define prq priority_queue
#define itr iterator
#define sf scanf
#define pf printf
#define pdb(prcs,x) (cout<<setprecision(prcs)<<fixed<<(sgn(x)?(x):0))
#ifdef DEBUG
#define prt(x) cerr<<#x"="<<(x)<<endl
#define asrtWA(s) do if(!(s))do{cerr<<"assert("#s")"<<endl;}whl(0);whl(0)
#define asrtTLE(s) do if(!(s))do{cerr<<"assert("#s")"<<endl;}whl(0);whl(0)
#define asrtMLE(s) do if(!(s))do{cerr<<"assert("#s")"<<endl;}whl(0);whl(0)
#define asrtOLE(s) do if(!(s))do{cerr<<"assert("#s")"<<endl;}whl(0);whl(0)
#define asrtRE(s) do if(!(s))do{cerr<<"assert("#s")"<<endl;}whl(0);whl(0)
#define runtime() cerr<<"Used: "<<db(clock())/CLOCKS_PER_SEC<<"s"<<endl
#define input(in) do{}whl(0)
#define output(out) do{}whl(0)
#else
#define endl (char('\n'))
#define prt(x) (cerr)
#define asrtWA(s) do if(!(s))exit(0);whl(0)
#define asrtTLE(s) do if(!(s))whl(1);whl(0)
#define asrtMLE(s) do if(!(s))whl(new int);whl(0)
#define asrtOLE(s) do if(!(s))whl(1)puts("OLE");whl(0)
#define asrtRE(s) do if(!(s))*(int*)0=0;whl(0)
#define runtime() (cerr)
#define input(in) freopen(in,"r",stdin)
#define output(out) freopen(out,"w",stdout)
#endif

typedef long long int lli;
typedef double db;
typedef const char* cstr;
typedef string str;
typedef vec<int> vi;
typedef vec<vi> vvi;
typedef vec<bool> vb;
typedef vec<vb> vvb;
typedef vec<str> vs;
typedef pr<int,int> pii;
typedef pr<lli,lli> pll;
typedef pr<db,db> pdd;
typedef map<int,int> mii;
typedef map<str,int> msi;
typedef map<char,int> mci;
typedef set<int> si;
typedef set<str> ss;
typedef que<int> qi;
typedef vec<pii> vpii;
typedef vec<pdd> vpdd;
#if __GNUC__>=4 and __GNUC_MINOR__>=7
template<typename key,typename value>class ext_map:public __gnu_pbds::tree<key,value,less<key>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>{};
template<typename key>class ext_set:public __gnu_pbds::tree<key,__gnu_pbds::null_type,less<key>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>{};
#elif __GNUC__>=4 and __GNUC_MINOR__>=6
template<typename key,typename value>class ext_map:public __gnu_pbds::tree<key,value,less<key>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>{};
template<typename key>class ext_set:public __gnu_pbds::tree<key,__gnu_pbds::null_mapped_type,less<key>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>{};
#endif

int oo=(~0u)>>1;
lli ooll=(~0ull)>>1;
db inf=1e+10;
db eps=1e-10;
db pi=acos(-1.0);
int dx[]={1,0,-1,0,1,-1,-1,1,0};
int dy[]={0,1,0,-1,1,1,-1,-1,0};
int MOD=1000000007;

template<typename type>inline bool cmax(type& a,const type& b){rtn a<b?a=b,true:false;}
template<typename type>inline bool cmin(type& a,const type& b){rtn b<a?a=b,true:false;}
template<typename type>inline type sqr(const type& x){rtn x*x;}
inline int sgn(const db& x){rtn (x>+eps)-(x<-eps);}
inline int dbcmp(const db& a,const db& b){rtn sgn(a-b);}
template<typename istream,typename first_type,typename second_type>inline istream& operator>>(istream& cin,pr<first_type,second_type>& x){rtn cin>>x.x>>x.y;}
template<typename ostream,typename first_type,typename second_type>inline ostream& operator<<(ostream& cout,const pr<first_type,second_type>& x){rtn cout<<x.x<<" "<<x.y;}
template<typename type>inline pr<type,type> operator-(const pr<type,type>& x){rtn mp(-x.x,-x.y);}
template<typename type>inline pr<type,type> operator+(const pr<type,type>& a,const pr<type,type>& b){rtn mp(a.x+b.x,a.y+b.y);}
template<typename type>inline pr<type,type> operator-(const pr<type,type>& a,const pr<type,type>& b){rtn mp(a.x-b.x,a.y-b.y);}
template<typename type>inline pr<type,type> operator*(const pr<type,type>& a,const type& b){rtn mp(a.x*b,a.y*b);}
template<typename type>inline pr<type,type> operator/(const pr<type,type>& a,const type& b){rtn mp(a.x/b,a.y/b);}
template<typename type>inline pr<type,type>& operator-=(pr<type,type>& a,const pr<type,type>& b){rtn a=a-b;}
template<typename type>inline pr<type,type>& operator+=(pr<type,type>& a,const pr<type,type>& b){rtn a=a+b;}
template<typename type>inline pr<type,type>& operator*=(pr<type,type>& a,const type& b){rtn a=a*b;}
template<typename type>inline pr<type,type>& operator/=(pr<type,type>& a,const type& b){rtn a=a/b;}
template<typename type>inline type cross(const pr<type,type>& a,const pr<type,type>& b){rtn a.x*b.y-a.y*b.x;}
template<typename type>inline type dot(const pr<type,type>& a,const pr<type,type>& b){rtn a.x*b.x+a.y*b.y;}
template<typename type>inline type gcd(type a,type b){if(b)whl((a%=b)&&(b%=a));rtn a+b;}
template<typename type>inline type lcm(type a,type b){rtn a*b/gcd(a,b);}
template<typename type>inline void bit_inc(vec<type>& st,int x,type inc){whl(x<sz(st))st[x]+=inc,x|=x+1;}
template<typename type>inline type bit_sum(const vec<type>& st,int x){type s=0;whl(x>=0)s+=st[x],x=(x&(x+1))-1;rtn s;}
template<typename type>inline type bit_kth(const vec<type>& st,int k){int x=0,y=0,z=0;whl((1<<(++y))<=sz(st));fdt(i,y-1,0){if((x+=1<<i)>sz(st)||z+st[x-1]>k)x-=1<<i;else z+=st[x-1];}rtn x;}
inline void make_set(vi& st){rep(i,sz(st))st[i]=i;}
inline int find_set(vi& st,int x){int y=x,z;whl(y!=st[y])y=st[y];whl(x!=st[x])z=st[x],st[x]=y,x=z;rtn y;}
inline bool union_set(vi& st,int a,int b){a=find_set(st,a),b=find_set(st,b);rtn a!=b?st[a]=b,true:false;}
template<typename type>inline void merge(type& a,type& b){if(sz(a)<sz(b))swap(a,b);whl(sz(b))a.insert(*b.begin()),b.erase(b.begin());}

struct Initializer{Initializer(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}~Initializer(){runtime();}}initializer;
/*
 * Package: StandardCodeLibrary.GraphTheory.MinCostMaxFlow
 * Usage:
 * MAXV:需要为点分配多少空间,点只要在0到MAXV-1就可以了，即MAXV应该大于最大编号
 * MAXE:需要为边分配多少空间,一条边对应一条正向边和一条反向边，即MAXE要等于实际最大边数*2
 * add_edge:
 * 输入int u,v,c,d
 * add_edge(u,v,c,d) 加一条u到v的容量为c代价为d的有向边,加一条v到u的容量为0代价为-d的有向边
 * build_graph:构图,详细见函数内的注释
 * min_cost_max_flow:
 * min_cost_max_flow(最大流,最小费用)
 * */
//#include <Core>

namespace StandardCodeLibrary
{
namespace GraphTheory
{
namespace MinCostMaxFlow
{

const lli oo=0x7f7f7f7f7f7f7f7fll;
const lli MAXE=1000000;
const lli MAXV=1000000;
typedef struct struct_edge* edge;
struct struct_edge{lli v,c,d;edge n,b;};
struct_edge pool[MAXE];
edge top;
lli S,T;
edge adj[MAXV];
void build_graph(lli s,lli t)
{
	top=pool,clr(adj);
	S=s,T=t;//源,汇
	//add_edge(u,v,c,d);
}
void add_edge(lli u,lli v,lli c,lli d)
{
	top->v=v,top->c=c,top->d=d,top->n=adj[u],adj[u]=top++;
	top->v=u,top->c=0,top->d=-d,top->n=adj[v],adj[v]=top++;
	adj[u]->b=adj[v],adj[v]->b=adj[u];
}
lli d[MAXV];
lli q[MAXV];
bool inq[MAXV];
lli qh,qt;
edge p[MAXV];
void min_cost_max_flow(lli& flow,lli& cost)
{
	flow=0,cost=0;
	lp
	{
		fl(d,oo),inq[q[qh=qt=0]=S]=true,d[S]=0,p[S]=0;
		whl(qh<=qt)
		{
			lli u=q[(qh++)%MAXV];
			inq[u]=false;
			for (edge i=adj[u];i;i=i->n)
				if (i->c&&cmin(d[i->v],d[u]+i->d))
				{
					if (!inq[i->v]) inq[q[(++qt)%MAXV]=i->v]=true;
					p[i->v]=i;
				}
		}
		if (d[T]==oo) break;
		else
		{
			lli delta=oo;
			for (edge i=p[T];i;i=p[i->b->v]) cmin(delta,i->c);
			for (edge i=p[T];i;i=p[i->b->v]) i->c-=delta,i->b->c+=delta;
			flow+=delta;
			cost+=d[T]*delta;
		}
	}
}

}
}
}
using namespace StandardCodeLibrary::GraphTheory::MinCostMaxFlow;

int main()
{
	inf=1e8;
	int n;
	cin>>n;
	vpii p(n);
	rep(i,n) cin>>p[i];
	int maxy=-::oo,cnt=0;
	rep(i,n) cmax(maxy,p[i].y);
	rep(i,n) if (p[i].y==maxy) cnt++;
	if (cnt!=1) cout<<-1<<endl;
	else
	{
		build_graph(n+n,n+n+1);
		rep(i,n)
		{
			add_edge(S,i,2,0);
			rep(j,n) if (p[j].y<p[i].y) add_edge(i,n+j,1,sqrt(sqr(p[i].x-p[j].x)+sqr(p[j].y-p[i].y))*inf);
			add_edge(n+i,T,1,0);
		}
		lli flow,cost;
		min_cost_max_flow(flow,cost);
		prt(flow);
		if (flow!=n-1) cout<<-1<<endl;
		else pdb(100,db(cost)/inf)<<endl;
	}
}