//#define READ_NUM_TEST_CASES
//#define ASSERTS		// force asserts on online judge
#define OLD_COMPILER

// (SOLUTION IS AT THE END OF THIS FILE)

////////////////////////// PROTOTYPING TEMPLATE /////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2012-2014
/*
    This program is licensed under GNU General Public License version 3.
    See <http://www.gnu.org/licenses/>.
*/
//
//

// enable c++ iostream; only if no fastio
//#define IOSTREAM

//#define NO_UNLOCKED	// fread_unlocked, fwrite_unlocked



#include<cstdint>
#include<utility>

namespace ab{

typedef int8_t i8;
typedef uint8_t ui8;
typedef int16_t i16;
typedef uint16_t ui16;
typedef int32_t i32;
typedef uint32_t ui32;
typedef int64_t i64;
typedef uint64_t ui64;


// old:
typedef i64 ll;
typedef ui64 ull;

typedef std::pair<i32,i32> pii;

typedef unsigned int uint;
typedef unsigned short ushort;
typedef unsigned char uchar;

struct VOID {};


template<typename I>struct FloatFrom{typedef VOID R;};
template<>struct FloatFrom<i32>{typedef double R;};
template<>struct FloatFrom<ui32>{typedef double R;};
template<>struct FloatFrom<i64>{typedef long double R;};
template<>struct FloatFrom<ui64>{typedef long double R;};
template<>struct FloatFrom<i16>{typedef float R;};
template<>struct FloatFrom<ui16>{typedef float R;};
template<>struct FloatFrom<i8>{typedef float R;};
template<>struct FloatFrom<ui8>{typedef float R;};
template<>struct FloatFrom<float>{typedef float R;};
template<>struct FloatFrom<double>{typedef double R;};
template<>struct FloatFrom<long double>{typedef long double R;};

template<typename I>struct Double{typedef VOID R;};
template<>struct Double<i8>{typedef i16 R;};
template<>struct Double<ui8>{typedef ui16 R;};
template<>struct Double<i16>{typedef i32 R;};
template<>struct Double<ui16>{typedef ui32 R;};
template<>struct Double<i32>{typedef i64 R;};
template<>struct Double<ui32>{typedef ui64 R;};

template<>struct Double<float>{typedef float R;};
template<>struct Double<double>{typedef double R;};
template<>struct Double<long double>{typedef long double R;};


#if defined __GNUC__ and ( __WORDSIZE == 64 )
typedef int128_t i128;
typedef uint128_t ui128;
template<>struct Double<i64>{typedef i128 R;};
template<>struct Double<ui64>{typedef ui128 R;};
#endif


}

#define FASTIO

#ifdef NO_FASTIO
#undef FASTIO
#endif

#ifdef DEBUG
#undef NDEBUG
#pragma message "Compiling in DEBUG mode."

#ifdef _WIN32
#include<windows.h>
inline void ec(int a){static HANDLE h=GetStdHandle(-12);SetConsoleTextAttribute(h,a?12:0xf);}
inline void oc(int a){static HANDLE h=GetStdHandle(-11);SetConsoleTextAttribute(h,a?10:0xf);}
#else
// *nix includes for debug
#endif

#else
#define NDEBUG
#define ec(x)
#define oc(x)
#endif



#include <cstdio>
#include <cfloat>



#define _CAT(a,b) a##b
#define CAT(a,b) _CAT(a,b)
#define _10TH(a,b,c,d,e,f,g,h,i,CNT,...) CNT
#define VA_CNT(...) _10TH(__VA_ARGS__,9,8,7,6,5,4,3,2,1)
#define VA_SEL(a,...) CAT(a,VA_CNT(__VA_ARGS__))(__VA_ARGS__)

#define _VA_GTONE(...) _10TH(__VA_ARGS__,1,1,1,1,1,1,1,1,0)
#define VA_GTONE(a,...) CAT(a,_VA_GTONE(__VA_ARGS__))(__VA_ARGS__)

#define foreach(e,c) for(auto&e:c)

#define  L0(str) 			fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__)
#define  L1(str,...)		fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__,__VA_ARGS__)

#define L(...) VA_GTONE(L,__VA_ARGS__)

#ifdef NDEBUG

#define D if(0)
#define A(x)
#define TEST_FLOAT(x)
#define ASSERT_FLOAT(x)

#else

#define A(x) assert(x);

#define _TEST_FLOAT(x) ((x) <= LDBL_MAX && (x) >= -LDBL_MAX)
#define ASSERT_FLOAT(f) A(_TEST_FLOAT(f))

#define D

#endif

#define V(x) (E<<#x<<": "<<(x)<<N)
#define XX {E<<"XX LINE "<<__LINE__<<N;}

#if defined DEBUG or defined ASSERTS
#undef NDEBUG
#else
#define NDEBUG
#endif

#ifdef _WIN32

// TODO
#ifndef NO_UNLOCKED
#define NO_UNLOCKED
#endif

//#define fread_unlocked _fread_nolock
//#define fwrite_unlocked _fwrite_nolock

#endif



#include<bits/stdc++.h>

#define mp make_pair
#define it iterator
#define be begin()
#define en end()
#define sz size()
#define fi first
#define se second
#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define all(x) (x).begin(),(x).end()
#define bs binary_search
#define lb lower_bound
#define ub upper_bound
#define type(x) __typeof(x)

#define fo3(i,a,b) for(int i=(int)(a); i<(int)(b); ++i)
#define of3(i,a,b) for(int i=(int)((b)-1); i>=(int)(a); --i)

#define fo2(i,n) fo3(i,0,n)
#define of2(i,n) of3(i,0,n)

#define fo(...) VA_SEL(fo,__VA_ARGS__)
#define of(...) VA_SEL(of,__VA_ARGS__)

#define inl		inline __attribute__ ((always_inline))
#define ninl	__attribute__ ((noinline))

const char N='\n';
const char S=' ';

using namespace std;
using namespace __gnu_cxx;

namespace ab{}
using namespace ab;



template<class T>inline T cbitl(T x,int i){return (x<<i) ^ (x>>(sizeof(T)*8-i));}

namespace std{
// 1,2,last (!!!!!)
template<>template<class A,class B>struct hash<map<A,B>>{
    size_t operator()(const map<A,B>& m) const{
        size_t r = m.size();
        if(!r)return r;
        auto i=m.be;
        r^=hash<type(i)>()(i);
        ++i;
        r^=cbitl(hash<type(i)>()(*i),sizeof(r)*8/4);
        i=m.end();
        --i;
        r^=cbitl(hash<type(i)>()(*i),sizeof(r)*8/2);
        return r;
    }
};
template<>template<class A, class B>struct hash<pair<A,B>>{
    size_t operator()(const pair<A,B>& p) const{
        return hash<A>()(p.first) ^ cbitl(hash<B>()(p.second),sizeof(size_t)*8/2);
    }
};
}

#define rint _rint()
#define ruint _ruint()
#define rll _rll()
#define rull _rull()
#define rchar _rchar()

#ifndef FASTIO
inline void fin(int){}inline void fout(int){}
#ifdef IOSTREAM
inline int _rint(){int r;cin>>r;return r;}
inline uint _ruint(){uint r;cin>>r;return r;}
inline ull _rull(){ull r;cin>>r;return r;}
inline char _rchar(){return cin.get();}
template<typename T>inline void W(const T& i){cout<<i;}
inline void W(){W('\n');}
#else
inline int _rint(){int r;scanf("%d",&r);return r;}
inline uint _ruint(){uint r;scanf("%u",&r);return r;}
inline ull _rull(){ull r;scanf("%llu",&r);return r;}
inline ull _rll(){ll r;scanf("%lld",&r);return r;}
inline char _rchar(){return getchar();}
inline void W(char a='\n'){printf("%c",a);}
inline void W(int a){printf("%d",a);}
inline void W(uint a){printf("%u",a);}
inline void W(const ull& a){printf("%llu",a);}
inline void W(const ll& a){printf("%lld",a);}
inline void W(const char *str){fputs(str,stdout);}
inline void W(const double& d){printf("%.20f",d);}
inline void W(const long double& d){printf("%.50Lf",d);}
#endif
#else

#ifndef NO_UNLOCKED
#define FREAD fread_unlocked
#define FWRITE fwrite_unlocked
#else
#define FREAD fread
#define FWRITE fwrite
#endif

// todo: test on pointers
const int _IB=32768;const int _OB=32768;
char _iB[_IB];int _iP = _IB;char _oB[_OB];int _oP = 0;
inline void fin(int mc){int r=_IB-_iP;if(r>mc)return;fo(i,r)_iB[i]=_iB[i+_iP];	// TODO: memcpy
    FREAD(_iB+r,1,_iP,stdin);_iP = 0;}
inline void fout(int mc){if(_OB-_oP>mc)return;FWRITE(_oB,1,_oP,stdout);_oP = 0;}
inline void W(char c='\n'){_oB[_oP++]=c;}
inline char _rchar(){return _iB[_iP++];}
template<class T>inline T _rur(){
    T r=0;char c=rchar;
    do c-='0',r=r*10+c,c=rchar;while(c>='0');
    return r;}
template<class T>inline T _rsi(){
	char c=rchar;
	while(c<'-')c=rchar;
	if(c=='-')return -_rur<T>();
	else{--_iP;return _rur<T>();}}
template<class T>inline T _ru(){while(rchar<'0');--_iP;return _rur<T>();}

inline int _rint(){fin(15);return _rsi<int>();}
inline uint _ruint(){fin(15);return _ru<uint>();}
inline ll _rll(){fin(25);return _rsi<ll>();}
inline ull _rull(){fin(25);return _ru<ull>();}

const int _rs = 20;char _r[_rs];
template<class T>inline void _w(T i){
	if(numeric_limits<T>::is_signed && i<0)W('-'),i=-i;
	else if(i==0){W('0');return;}
	int pos = _rs;
	do{_r[--pos]='0'+i%10;i/=10;}while(i);
	do W(_r[pos]),++pos;while(pos<_rs);}
inline void W(const int32_t& i){fout(15);_w(i);}
inline void W(const uint32_t& i){fout(15);_w(i);}
inline void W(const int64_t& i){fout(25);_w(i);}
inline void W(const uint64_t& i){fout(25);_w(i);}
inline void W(const char*str){int l=strlen(str);fout(l);memcpy(&_oB[_oP],str,l);_oP+=l;}
inline void W(double d){fout(50);_oP+=sprintf(&_oB[_oP],"%.20f",d);}	// todo
#endif
template<class A,class B>inline void W(const A&a,const B&b){W(a);W(b);}
template<class A,class B,class C>
inline void W(const A&a,const B&b,const C&c){W(a);W(b);W(c);}
template<class A,class B,class C,class DD>
inline void W(const A&a,const B&b,const C&c,const DD&dd){W(a);W(b);W(c);W(dd);}
template<class T>inline void sortall(T&t){sort(t.be,t.en);}
template<class T>inline void uniqueall(T&t){t.resize(unique(t.be,t.en));}

inline int count1(uint i){return __builtin_popcount(i);}
inline int count1(ull i){return __builtin_popcountll(i);}
inline int parity(uint i){return __builtin_parity(i);}
inline int parity(ull i){return __builtin_parityll(i);}
inline int ilog(uint i){return 31-__builtin_clz(i);} // int log; floor(log2(i))
inline int ilog(ull i){return 63-__builtin_clzll(i);}
#define powerof2(x) !(x&(x-1))
#define subset(a,b) (a&b==a)
#define kbegin(k) ((1<<k)-1)
#define kend(k,n) ((kbegin(k)<<n-k)+1)
inline uint knext(uint a){uint b=(a|(a-1))+1;return b|((a^b)>>(__builtin_ctz(a)+2));}
#define fors(x,k,n) for(uint x=kbegin(k);x<kend(k,n);x=knext(x))


template<class A,class B>inline ostream&operator<<(ostream&o,const pair<A,B>&p){o<<'<'<<p.fi<<", "<<p.se<<'>';return o;}
template<class A,class B>inline ostream&operator<<(ostream&o,const map<A,B>&m){o<<N;for(auto&k:m)o<<"map["<<k.fi<<"] -> "<<k.se<<N;return o;}
template<class A>inline ostream&operator<<(ostream&o,const vector<A>&v){o<<N;fo(i,v.sz)o<<"vector["<<i<<"] = "<<v[i]<<N;return o;}

struct _O{template<class T>_O&operator<<(const T&t){oc(1);W(t);oc(0);return*this;}}O;
struct _I{
	_I&operator>>(int32_t&t){t=rint;return*this;}
	_I&operator>>(uint32_t&t){t=ruint;return*this;}
	_I&operator>>(int64_t&t){t=rll;return*this;}
	_I&operator>>(uint64_t&t){t=rull;return*this;}
}I;

struct _E{template<class T>_E&operator<<(const T&t){D{ec(1);cerr<<t;ec(0);}return*this;}}E;



inline void tc();
int main()
{
#ifdef FASTIO
    setvbuf(stdin,0,_IONBF,0);setvbuf(stdout,0,_IONBF,0);
#elif defined IOSTREAM
	ios_base::sync_with_stdio(0);cin.tie(0);cout.precision(99);cout.setf(ios::fixed,ios::floatfield);
#endif

#ifdef DEBUG
#ifdef _WIN32
	ec(0);
	oc(0);
#else
// TODO: *nix
#endif
#endif
	
#ifdef READ_NUM_TEST_CASES
	int nz=rint;fo(i,nz)
#endif
	tc();
#ifdef FASTIO
    FWRITE(_oB,1,_oP,stdout);
#endif
	return 0;
}
// END OF TEMPLATE














#include<type_traits>

namespace ab
{


template<bool cond, typename T, typename F> struct IF {typedef T R;};
template<typename T, typename F> struct IF<false,T,F> {typedef F R;};

template <bool B, class T = void> struct ENABLE_IF {typedef T R;};
template <class T> struct ENABLE_IF<false, T> {};

template <bool B, class T = void> struct DISABLE_IF {typedef T RET;};
template <class T> struct DISABLE_IF<true, T> {};



template<typename A, typename B>
struct SAME_TYPE
{
	static const bool RET = false;
};
template<typename T>
struct SAME_TYPE<T,T>
{
	static const bool RET = true;
};


template<typename T>
struct IS_CLASS
{
	template<typename C> static char (&f(int C::*))[1];
	template<typename C> static char (&f(...))[2];

	static bool const R = sizeof(f<T>(0))==1;
};



struct FALSE
{
	static bool const R = false;
};

template<class T>
struct RR{
typedef typename std::remove_reference<T>::type R;
};


// get &T::x or &T::first
template<class T,class=void>struct GET_X{};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::x)>::value>::type>{typedef decltype(&T::x) R;};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::first)>::value>::type>{typedef decltype(&T::first) R;};

// get &T::y or &T::second
template<class T,class=void>struct GET_Y{};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::y)>::value>::type>{typedef decltype(&T::y) R;};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::second)>::value>::type>{typedef decltype(&T::second) R;};






}


namespace ab{

/////////////////////////////// STATIC ARRAY ///////////////////////////////////
// requires: TEMPLATES
//
// Copyright (c) 2013 by Adam Blaszkiewicz. All rights reserved.
//
template<typename T, int _capacity>
class StaticArray
{
public:
	StaticArray() : mSize(0) {}
	StaticArray(unsigned int _size) : mSize(_size) {A(_size<=_capacity);}
	inline void push_back(const T& t) {new(&mData()[mSize]) T(t); ++mSize;}
	inline void push_back() {new(&mData()[mSize]) T; ++mSize;}
	inline void pop_back() {A(mSize>0); --mSize; mData()[mSize].~T();}
	inline T& operator[](const int idx) {return mData()[idx];}
	inline const T& operator[](const int idx) const {A(idx<mSize); return mData()[idx];}
	inline T& back() {A(mSize>0); return mData()[mSize-1];}
	inline const T& back() const {A(mSize>0); return mData()[mSize-1];}
	inline T& front() {A(mSize>0); return mData()[0];}
	inline const T& front() const {A(mSize>0); return mData()[0];}
	inline int size() const {return mSize;}
	inline unsigned int capacity() const {return _capacity;}
	inline void resize(int newSize)
	{
		A(newSize <= _capacity);
		if(newSize > mSize) new (&mData()[mSize]) T[newSize-mSize];
		else for(int i=newSize; i<mSize; ++i) mData()[i].~T();
		mSize = newSize;
	}
	inline void reserve(int howMuch) const {A(howMuch <= _capacity);}
	inline void clear() {for(int i=0; i<mSize; ++i) mData()[i].~T(); mSize=0;}
	typedef T* iterator;
	inline iterator begin() {return mData;}
	inline iterator end()   {return mData+mSize;}
private:
	T* mData() {return reinterpret_cast<T*>(_mData);}
	char _mData[_capacity*sizeof(T)];
	int mSize;
};

// vector of at most n elements
template<typename T, int n> struct _vector
{typedef typename IF<n==0,std::vector<T>,StaticArray<T,n> >::R R;};
////////////////////////////////////////////////////////////////////////////////

}


namespace ab{


////////////////////////////////////////////////////////////////////////////////
///////////////////////////////// GRAFY ////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////






////////////////////////////////////////////////////////////////////////////////
// BINDER
template<typename Ret, typename T>
class Binder
{
public:
	Binder(Ret T::*_var) : var(_var) {}
	Ret& operator()(T& obj) const
	{
		return obj.*var;
	}
	const Ret& operator()(const T& obj) const
	{
		return obj.*var;
	}
private:
	Ret T::*var;
};
template<typename Ret, typename T>
Binder<Ret,T> bind(Ret T::*var)
{
	return Binder<Ret,T>(var);
}
////////////////////////////////////////////////////////////////////////////////






////////////////////////////////////////////////////////////////////////////////
// KLASY GRAFOW //
// * wska┼║niki (PE, PV) i iteratory nie mog─ů du┼╝o zajmowa─ç,
//   bo mog─ů by─ç pami─Ötane przez np. Dinica
// * Dlatego s─ů to prawie (ca┼ékiem?) go┼ée wska┼║niki, kt├│re nie zawsze pozwalaj─ů
//   na wykonanie ┼╝─ůdanej operacji na tym, na co wskazuj─ů, np. usuwania kraw─Ödzi
// * Po to s─ů klasy VC i EC (context), kt├│re pozwalaj─ů wykonywa─ç
//   wszystkie dost─Öpne operacje
/*

template<uint _NMax = 0, uint _MMax = 0, typename _VExtra = VOID, typename _EExtra = VOID>
class G
{
public:
	static const uint NMax = _NMax;
	static const uint MMax = _MMax;
	typename _VExtra VExtra;
	typename _EExtra EExtra;

	struct VC//ontext
	{
		struct TO<E>
		{
			struct iterator : public PE
			{
				// ...
			};
			iterator begin();
			iterator end();

			EContext operator[](PE&);
		} to;
	};
	}

	struct EC//ontext
	{
		EExtra& operator->()
		VContext fr();
		VContext to();
		EContext rev() const;		// rev must be enabled
		bool revEnabled() const;
		void erase();
		void disable();				// EC becomes invalid
		void enableRev();			// rev must be disabled
	}


	struct PE;

	struct VS<V>
	{
		struct iterator : public PV
		{
			// ...
		};
		iterator begin();
		iterator end();

		VContext operator[](PV&);
	} vs;

	struct ES<E>
	{
		struct iterator : public PE
		{
			// ...
		};
		iterator begin();
		iterator end();

		EContext operator[](PE&);
	} es;

	struct V : public VExtra
	{
		V(VContext);
	};
	struct E : public EExtra
	{
		E(EContext);
	};
};
*/
////////////////////////////////////////////////////////////////////////////////




////////////////////////////////////////////////////////////////////////////////
// 2014-05-12
//              Vs			Es
// Iterate		no			yes
// Erase		no			no
// point		int			pointer
// rev						no
//
// Avoid vs reallocation! (?)
//
// Good for: Kruskal
//
// dummy vertices
//
template<typename VExtra=VOID, typename EExtra=VOID, uint NMax=0, uint MMax=0> class GraphU_EI{};
template<typename _EExtra, uint _NMax, uint _MMax>
class GraphU_EI<VOID,_EExtra,_NMax,_MMax>	// edges iterable
{
private:
	class V; class E;
	
public:
	static const uint NMax = _NMax;
	static const uint MMax = _MMax;
	typedef VOID VExtra;
	typedef _EExtra EExtra;
	typedef uint PV; typedef E* PE;
	
private:
	class V : public VExtra{
	};
	class E : public EExtra{
		friend class GraphU_EI;
		E(const PV& _fr, const PV& _to, const EExtra& eExtra) : EExtra(eExtra), fr(_fr), to(_to) {}
		PV fr,to;
	};
	
public:
	class VC; class EC; class VS; class ES;
	
	class VC{
	public:
		VC(GraphU_EI&_g, const PV& _v) : g(_g), v(_v){}
		operator PV()const{return v;}
	private:
		GraphU_EI& g;
		PV v;
	};
	class EC{
	public:
		EExtra* operator->(){return e;}
		template<class T> decltype(PE()->*T()) operator->*(const T& t){return e->*t;}
		operator PE()const{return e;}
		VC fr(){return VC(g,e->fr);}
		VC to(){return VC(g,e->to);}
		void fr(const PV& _fr){e->fr=_fr;}
		void to(const PV& _to){e->to=_to;}
		EC(GraphU_EI&_g, const PE& _e) : g(_g), e(_e) {}
	private:
		GraphU_EI& g;
		PE e;
	};
	
	class VS{
		friend class GraphU_EI;
	public:
		typedef uint iterator;
		uint size()const{return g.vsSize;}
		void resize(uint _size){g.vsSize=_size;}
		iterator begin()const{return 0;}
		iterator end()const{return g.vsSize;}
	private:
		GraphU_EI& g;
		VS(GraphU_EI& _g) : g(_g) {}
	} vs;
	
	class ES{
		friend class GraphU_EI;
	public:
		typedef PE iterator;
		inline iterator begin() {return &*g._es.begin();}
		inline iterator end()   {return &*g._es.end();}
		
		inline uint size()const{return g._es.size();}
		inline void resize(unsigned int _size) {g._es.resize(_size);}
		inline void reserve(unsigned int _size) {g._es.reserve(_size);}
		
		inline void push_back(const PV& from, const PV& to, const EExtra& eExtra = EExtra()){
			g._es.push_back(E(from,to,eExtra));
		}

		inline EC operator[](const PE& pe) {return EC(g,pe);}
		inline EC operator[](unsigned int idx){
			A(MMax==0 || idx < MMax);
			return EC(g,&g._es[idx]);
		}
	private:
		GraphU_EI& g;
		ES(GraphU_EI& _g) : g(_g) {}
	} es;
	
	GraphU_EI() : vs(*this), es(*this), vsSize(0) {}
	
private:
	typedef typename _vector<E,NMax>::R _ES;
	_ES _es;
	uint vsSize;
};




////////////////////////////////////////////////////////////////////////////////
// 2013-11-15
//              Vs			Es
// Iterate		yes			no
// Erase		no			yes
// point		pointer		pointer
// rev						yes
//
// Avoid vs reallocation!
// Es paired or single
//
// Good for: Dinic
//
// use BaseG::VExtra
// otherwise use G
template<typename _VExtra = VOID, typename _EExtra = VOID, uint _NMax = 0, uint _MMax = 0>
class BaseGraphU_ERD
{
public:
	static const uint NMax = _NMax;
	static const uint MMax = _MMax;
	typedef _VExtra VExtra;
	typedef _EExtra EExtra;

private:
	class V; class E;

public:
	typedef V* PV;
	typedef E* PE;

	typedef typename _vector<V,NMax>::R _VS;
public:
	inline BaseGraphU_ERD(_VS& __vs) : _vs(__vs), vs(*this) {}
	_VS& _vs;
private:
	struct E : public EExtra
	{
		inline E(const PV& _to, const PE& _rev, const EExtra& ee = EExtra()) :
			EExtra(ee), to(_to), rev(_rev) {}
		inline E(const E& o) : EExtra(o), to(o.to), rev(o.rev)
		{
			if(rev) rev->rev = this;
		}
		inline E& operator=(const E& o)
		{
			EExtra::operator=(o);
			to = o.to;
			rev = o.rev;
			if(rev) rev->rev = this;
			return *this;
		}
		PV to;
		PE rev;
	};

	class V : public VExtra
	{
		friend class BaseGraphU_ERD;
	private:
		std::vector<E> to;
	};

	//_VS& _vs;


public:
	class VC; class EC; class VS;

	class VC//ontext
	{
		friend class VS;
		friend class EC;
	public:
		struct TO
		{
			friend class BaseGraphU_ERD;
		private:
			BaseGraphU_ERD& g;
			PV pv;
			inline TO(BaseGraphU_ERD& _g, PV& _pv) : g(_g), pv(_pv) {}
			inline void push_back(const E& e)
			{
				pv->to.push_back(e);
			}
		public:
			typedef PE iterator;
			inline iterator begin() {return &*pv->to.begin();}
			inline iterator end()   {return &*pv->to.end();}
			inline void reserve(unsigned int size) {pv->to.reserve(size);}
			inline E& back() {return pv->to.back();}
			inline const E& back() const {return pv->to.back();}
			inline E& front() {return pv->to.front();}
			inline const E& front() const {return pv->to.front();}

			inline EC operator[](PE& pe)
			{
				return EC(g,pe,pv);
			}
		} to;

		inline V& operator*() {return *to.pv;}
		inline const V& operator*() const {return *to.pv;}
		inline V* operator->() {return to.pv;}
		inline const V* operator->() const {return to.pv;}
		inline operator PV() const {return to.pv;}
	private:
		inline VC(BaseGraphU_ERD& _g, PV _pv) : to(_g,_pv) {}
	};


	class EC//ontext
	{
		friend class VC::TO;
	public:
		inline VC to() const {return VC(g,pe->to);}
		inline EC rev() const {return EC(g,pe->rev,pe->to);}		// rev must be enabled
		inline bool revEnabled() const {return pe->rev != 0;}
		inline void delSingle()
		{
			A(!pe->rev);	// single
			g._delE(pvfrom,pe);
		}
		inline void delPaired()
		{
			g._delE(pe->to, pe->rev);
			g._delE(pvfrom, pe);
		}
		inline void del()	// !!! SLOWER !!!
		{
			if(pe->rev) _delE(pe->to, pe->rev);
			g._delE(pvfrom, pe);
		}
		inline void disable()	// EC becomes invalid, rev must be enabled
		{
			PE reve = pe->rev;
			g._delE(pvfrom, pe);
			reve->rev = 0;
		}
		inline void enableRev()	// rev must be disabled
		{
			A(pe->rev==0);
			pe->rev = &*pe->to->to.begin() + pe->to->to.size();
			pe->to->to.push_back(E(pvfrom,pe));
		}

		inline operator PE() const {return pe;}
	private:
		inline EC(BaseGraphU_ERD& _g, const PE& _pe, const PV& _pvfrom) :
			g(_g), pe(_pe), pvfrom(_pvfrom) {}
		BaseGraphU_ERD& g;
		PE pe;
		PV pvfrom;
	};

	class VS
	{
		friend class BaseGraphU_ERD;
	public:
		typedef PV iterator;
		inline iterator begin() {return &*g._vs.begin();}
		inline iterator end()   {return &*g._vs.end();}

		inline void resize(unsigned int size) {g._vs.resize(size);}

		inline VC operator[](const PV& pv) {return VC(g,pv);}
		inline VC operator[](unsigned int idx)
		{
			A(NMax==0 || idx < NMax);
			return VC(g,&g._vs[idx]);
		}
	private:
		BaseGraphU_ERD& g;
		VS(BaseGraphU_ERD& _g) : g(_g) {}
	} vs;

	inline void addSingle(PV vot, PV vto, EExtra extra = EExtra())
	{
		vot->to.push_back(E(vto,0,extra));
	}

	inline void addPaired(const PV& vot, const PV& vto, const EExtra& extra1 = EExtra(), const EExtra& extra2 = EExtra())
	{
		vot->to.push_back(E(vto,0,extra1));
		vto->to.push_back(E(vot,0,extra2));
		vot->to.back().rev = &*vto->to.begin()+vto->to.size()-1;
		vto->to.back().rev = &*vot->to.begin()+vot->to.size()-1;
		/*
		vs[vot].to.push_back();
		E& e1 = vs[vot].to.back();
		vs[vto].to.push_back();
		E& e2 = vs[vto].to.back();
		e1.~E();	// avoid copy constructors
		new(&e1) E(vto, &e2, extra1);
		e2.~E();
		new(&e2) E(vot, &e1, extra2);*/
	}
private:
	inline void _delE(const PV& pvfrom, const PE& pe)
	{
		*pe = pvfrom->to.back();
		pvfrom->to.pop_back();
	}
};
template<typename _VExtra = VOID, typename _EExtra = VOID, uint _NMax = 0, uint _MMax = 0>
class GraphU_ERD	// edges removable, disableable
	: public BaseGraphU_ERD<_VExtra,_EExtra,_NMax,_MMax>//raphU_ERD
{
public:
	typedef BaseGraphU_ERD<_VExtra,_EExtra,_NMax,_MMax> BASE;
	inline GraphU_ERD() : BASE(__vs) {}
	typename BASE::_VS __vs;
};
////////////////////////////////////////////////////////////////////////////////





}




#include<cstring>
#include<vector>

namespace ab{

////////////////////////////////// UNION FIND //////////////////////////////////
class UnionFind
{
public:
	UnionFind(size_t univSize) : parents(univSize), ranks(univSize,0)
	{
		for(size_t i=0; i<univSize; ++i) parents[i] = i;
	}
	size_t find(size_t x)
	{
		size_t root = x;
		while(parents[root] != root) root = parents[root];
		while(x != root)
		{
			size_t& curr = parents[x];
			x = parents[x];
			curr = root;
		}
		return root;
	}
	bool makeUnion(size_t a, size_t b) // false if union already made
	{
		a = find(a);
		b = find(b);
		if(a==b)return false;
		if(ranks[a] < ranks[b]) parents[a] = b, ++ranks[b];
		else parents[b] = a, ++ranks[a];
		return true;
	}
private:
	std::vector<size_t> parents;
	std::vector<size_t> ranks;
};
////////////////////////////////////////////////////////////////////////////////

}


namespace ab
{
	// MST
	// O(m log n)
	//
	// minNumComponents is optional, for optimization; setting lower than actual number of components is ok
	//
	// zeroResult=false wydaje sie nic nie przyspieszac
	//
	// sorted=true znacznie przyspiesza. mo┐na u┐yŠ counting sorta wczesniej
	//
	#ifdef OLD_COMPILER
	template<typename G, typename EWeight, typename EResult, bool sorted = false, bool zeroResult=true, int minNumComponents = 1>
	#else
	template<bool sorted = false, bool zeroResult=true, int minNumComponents = 1, typename G, typename EWeight, typename EResult>
	#endif
	int kruskal(G& g, const EWeight& eWeight, const EResult& eResult)
	{
		unsigned int numEdges = g.es.size();
		unsigned int numVerts = g.vs.size();
		
		if(!sorted)std::sort(g.es.begin(),g.es.end(),[eWeight](const typename G::EExtra& a, const typename G::EExtra& b){return a.*eWeight < b.*eWeight;});
		
		UnionFind uf(numVerts);
		int numFound = 0;
		
		int i=0;
		for(; i<numEdges && numFound < numVerts-minNumComponents; ++i)
		{
			typename G::PV a = g.es[i].fr();
			typename G::PV b = g.es[i].to();
			int aa = uf.find(a-g.vs.begin());
			int bb = uf.find(b-g.vs.begin());
			if(aa==bb){
				if(zeroResult)g.es[i]->*eResult = false;
				continue;
			}
			
			uf.makeUnion(aa,bb);
			++numFound;
			g.es[i]->*eResult = true;
		}
		if(zeroResult) for(;i<numEdges;++i) g.es[i]->*eResult = false;
		
		return numFound;
	}
	
	#ifdef OLD_COMPILER
	template<typename G, typename EWeight, bool sorted = false, unsigned int minNumComponents = 1>
	#else
	template<bool sorted = false, unsigned int minNumComponents = 1, typename G, typename EWeight>
	#endif
	std::vector<typename G::PE> kruskal(G& g, const EWeight& eWeight)
	{
		unsigned int numEdges = g.es.size();
		unsigned int numVerts = g.vs.size();
		
		if(!sorted)std::sort(g.es.begin(),g.es.end(),[eWeight](const typename G::EExtra& a, const typename G::EExtra& b){return a.*eWeight < b.*eWeight;});
		
		UnionFind uf(numVerts);
		std::vector<typename G::PE> result;
		result.reserve(numVerts-minNumComponents);
		
		for(int i=0; i<numEdges && result.size() < numVerts-minNumComponents; ++i)
		{
			typename G::PV a = g.es[i].fr();
			typename G::PV b = g.es[i].to();
			int aa = uf.find(a-g.vs.begin());
			int bb = uf.find(b-g.vs.begin());
			if(aa==bb)continue;
			
			uf.makeUnion(aa,bb);
			result.push_back(g.es[i]);
		}
		
		return result;
	}
	
	
	template<typename Weight>
	struct _boruvkaCleanupEdge
	{
		int from;
		int to;
		Weight val;
		int orig;
		
		static int getFrom(const _boruvkaCleanupEdge& e)
		{
			return e.from;
		}
		static int getTo(const _boruvkaCleanupEdge& e)
		{
			return e.to;
		}
	};
	/*
	// MST
	// sets resultEDataKey to true for edges in MST, does not set resultEDataKey for other edges
	// O(min(m log n, n^2))
	// O(n) if planar
	// set cleanupfirst = false if there are no multiple (u,v) edges
	// Old paper by Cheriton, ...
	template<bool cleanupFirst = true, typename G, typename EWeight>
	std::vector<G::PE> boruvkaCleanup(G& g, const EWeight& eWeight)
	{
		int numTrees = g.vs.size();
		
		std::vector<_boruvkaCleanupEdge<Weight>> edges(g.edges.size());
		for(unsigned int i=0; i<g.edges.size(); ++i)
		{
			edges[i].from = g.edges[i].from;
			edges[i].to   = g.edges[i].to;
			edges[i].val  = getWeightEData(g.edges[i]);
			edges[i].orig = i;
		}
		
		std::pair<int,Weight> *bests = new std::pair<int,Weight>[numTrees];
		int *vmap = new int[numTrees];
		
		int numFound = 0;
		
		for(;;)
		{
			// cleanup
			if(numFound != 0 || cleanupFirst)
			{
				std::vector<_boruvkaCleanupEdge<Weight> > helperEdges(edges.size());
				countingSort(&edges[0], &edges[0] + edges.size(), &helperEdges[0], numTrees, _boruvkaCleanupEdge<Weight>::getTo);
				countingSort(&helperEdges[0], &helperEdges[0] + edges.size(), &edges[0], numTrees, _boruvkaCleanupEdge<Weight>::getFrom);
				int curDest = 0;
				int prev1 = -1;
				int prev2 = -1;
				Weight bestval = 0;
				int bestarg = 0;
				//printf("edges size %d\n", edges.size());
				for(unsigned int i=0; i<edges.size(); ++i)
				{
					int n1 = edges[i].from;
					int n2 = edges[i].to;
					
					if(n1 == n2) continue;
					
					if(prev1 == n1 && prev2 == n2)
					{
						if(edges[i].val < bestval) bestval = edges[i].val, bestarg = i;
					}
					else
					{
						if(prev1 != -1) edges[curDest++] = edges[bestarg];
						bestval = edges[i].val;
						bestarg = i;
						prev1 = n1;
						prev2 = n2;
					}
				}
				if(prev1 != -1) edges[curDest++] = edges[bestarg];
				edges.resize(curDest);
			}
			//cleanup end
			
			//printf("Cheriton step: %d trees, %d edges, found %d\n",numTrees,edges.size(),numFound);
			
			// find bests
			memset(bests, 0xff, sizeof(std::pair<int,Weight>)*numTrees);
			for(unsigned int i=0; i<edges.size(); ++i)
			{
				//printf("%x\n",bests[a].first);
				int a = edges[i].from;
				if((unsigned int)bests[a].first == 0xffffffff || bests[a].second > edges[i].val)
				{
					bests[a].second = edges[i].val;
					bests[a].first = i;
				}
				
				int b = edges[i].to;
				if((unsigned int)bests[b].first == 0xffffffff || bests[b].second > edges[i].val)
				{
					bests[b].second = edges[i].val;
					bests[b].first = i;
				}
			}
			// find bests end
		
			UnionFind uf(numTrees);
			bool change = false;
			for(int i=0; i<numTrees; ++i)
			{
				int best = bests[i].first;
				if((unsigned int)best == 0xffffffff) continue;
				
				int a = edges[best].from;
				int b = edges[best].to;
				a = uf.find(a);
				b = uf.find(b);
				if(a==b)continue;
				
				uf.makeUnion(a,b);
				getResultEData(g.edges[edges[best].orig]) = true;
				++numFound;
				change = true;
			}
			
			if(!change) break;
			
			// przemianowanie
			int newNumTrees = 0;
			memset(vmap, 0xff, sizeof(int)*numTrees);
			for(int i=0; i<numTrees; ++i)
			{
				int a = uf.find(i);
				if((unsigned int)vmap[a] == 0xffffffff) vmap[a] = newNumTrees++;
				vmap[i] = vmap[a];
			}
			for(unsigned int i=0; i<edges.size(); ++i)
			{
				edges[i].from = vmap[edges[i].from];
				edges[i].to   = vmap[edges[i].to];
			}
			numTrees = newNumTrees;
			// przemianowanie end
		}
		
		delete[] bests;
		delete[] vmap;
		return numFound;
	}
	*/
}


struct EExtra{
	int weight;
};
typedef GraphU_EI<VOID,EExtra> G;

inline void tc()
{
	uint n;
	I>>n;
	
	G g;
	g.vs.resize(n+1);
	g.es.reserve(n*(n+1)/2);
	fo(i,n)fo(j,i+1,n+1){
		int val = rint;
		g.es.pub(i,j,EExtra{val});
	}
	
	auto result = kruskal(g,&EExtra::weight);
	A(result.sz+1 == n);	// tree
	
	ui64 r = 0;
	fo(i,result.sz)r += result[i]->weight;
	
	O<<r<<N;
}

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//#define READ_NUM_TEST_CASES
//#define ASSERTS		// force asserts on online judge
#define OLD_COMPILER

// (SOLUTION IS AT THE END OF THIS FILE)

////////////////////////// PROTOTYPING TEMPLATE /////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2012-2014
/*
    This program is licensed under GNU General Public License version 3.
    See <http://www.gnu.org/licenses/>.
*/
//
//

// enable c++ iostream; only if no fastio
//#define IOSTREAM

//#define NO_UNLOCKED	// fread_unlocked, fwrite_unlocked



#include<cstdint>
#include<utility>

namespace ab{

typedef int8_t i8;
typedef uint8_t ui8;
typedef int16_t i16;
typedef uint16_t ui16;
typedef int32_t i32;
typedef uint32_t ui32;
typedef int64_t i64;
typedef uint64_t ui64;


// old:
typedef i64 ll;
typedef ui64 ull;

typedef std::pair<i32,i32> pii;

typedef unsigned int uint;
typedef unsigned short ushort;
typedef unsigned char uchar;

struct VOID {};


template<typename I>struct FloatFrom{typedef VOID R;};
template<>struct FloatFrom<i32>{typedef double R;};
template<>struct FloatFrom<ui32>{typedef double R;};
template<>struct FloatFrom<i64>{typedef long double R;};
template<>struct FloatFrom<ui64>{typedef long double R;};
template<>struct FloatFrom<i16>{typedef float R;};
template<>struct FloatFrom<ui16>{typedef float R;};
template<>struct FloatFrom<i8>{typedef float R;};
template<>struct FloatFrom<ui8>{typedef float R;};
template<>struct FloatFrom<float>{typedef float R;};
template<>struct FloatFrom<double>{typedef double R;};
template<>struct FloatFrom<long double>{typedef long double R;};

template<typename I>struct Double{typedef VOID R;};
template<>struct Double<i8>{typedef i16 R;};
template<>struct Double<ui8>{typedef ui16 R;};
template<>struct Double<i16>{typedef i32 R;};
template<>struct Double<ui16>{typedef ui32 R;};
template<>struct Double<i32>{typedef i64 R;};
template<>struct Double<ui32>{typedef ui64 R;};

template<>struct Double<float>{typedef float R;};
template<>struct Double<double>{typedef double R;};
template<>struct Double<long double>{typedef long double R;};


#if defined __GNUC__ and ( __WORDSIZE == 64 )
typedef int128_t i128;
typedef uint128_t ui128;
template<>struct Double<i64>{typedef i128 R;};
template<>struct Double<ui64>{typedef ui128 R;};
#endif


}

#define FASTIO

#ifdef NO_FASTIO
#undef FASTIO
#endif

#ifdef DEBUG
#undef NDEBUG
#pragma message "Compiling in DEBUG mode."

#ifdef _WIN32
#include<windows.h>
inline void ec(int a){static HANDLE h=GetStdHandle(-12);SetConsoleTextAttribute(h,a?12:0xf);}
inline void oc(int a){static HANDLE h=GetStdHandle(-11);SetConsoleTextAttribute(h,a?10:0xf);}
#else
// *nix includes for debug
#endif

#else
#define NDEBUG
#define ec(x)
#define oc(x)
#endif



#include <cstdio>
#include <cfloat>



#define _CAT(a,b) a##b
#define CAT(a,b) _CAT(a,b)
#define _10TH(a,b,c,d,e,f,g,h,i,CNT,...) CNT
#define VA_CNT(...) _10TH(__VA_ARGS__,9,8,7,6,5,4,3,2,1)
#define VA_SEL(a,...) CAT(a,VA_CNT(__VA_ARGS__))(__VA_ARGS__)

#define _VA_GTONE(...) _10TH(__VA_ARGS__,1,1,1,1,1,1,1,1,0)
#define VA_GTONE(a,...) CAT(a,_VA_GTONE(__VA_ARGS__))(__VA_ARGS__)

#define foreach(e,c) for(auto&e:c)

#define  L0(str) 			fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__)
#define  L1(str,...)		fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__,__VA_ARGS__)

#define L(...) VA_GTONE(L,__VA_ARGS__)

#ifdef NDEBUG

#define D if(0)
#define A(x)
#define TEST_FLOAT(x)
#define ASSERT_FLOAT(x)

#else

#define A(x) assert(x);

#define _TEST_FLOAT(x) ((x) <= LDBL_MAX && (x) >= -LDBL_MAX)
#define ASSERT_FLOAT(f) A(_TEST_FLOAT(f))

#define D

#endif

#define V(x) (E<<#x<<": "<<(x)<<N)
#define XX {E<<"XX LINE "<<__LINE__<<N;}

#if defined DEBUG or defined ASSERTS
#undef NDEBUG
#else
#define NDEBUG
#endif

#ifdef _WIN32

// TODO
#ifndef NO_UNLOCKED
#define NO_UNLOCKED
#endif

//#define fread_unlocked _fread_nolock
//#define fwrite_unlocked _fwrite_nolock

#endif



#include<bits/stdc++.h>

#define mp make_pair
#define it iterator
#define be begin()
#define en end()
#define sz size()
#define fi first
#define se second
#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define all(x) (x).begin(),(x).end()
#define bs binary_search
#define lb lower_bound
#define ub upper_bound
#define type(x) __typeof(x)

#define fo3(i,a,b) for(int i=(int)(a); i<(int)(b); ++i)
#define of3(i,a,b) for(int i=(int)((b)-1); i>=(int)(a); --i)

#define fo2(i,n) fo3(i,0,n)
#define of2(i,n) of3(i,0,n)

#define fo(...) VA_SEL(fo,__VA_ARGS__)
#define of(...) VA_SEL(of,__VA_ARGS__)

#define inl		inline __attribute__ ((always_inline))
#define ninl	__attribute__ ((noinline))

const char N='\n';
const char S=' ';

using namespace std;
using namespace __gnu_cxx;

namespace ab{}
using namespace ab;



template<class T>inline T cbitl(T x,int i){return (x<<i) ^ (x>>(sizeof(T)*8-i));}

namespace std{
// 1,2,last (!!!!!)
template<>template<class A,class B>struct hash<map<A,B>>{
    size_t operator()(const map<A,B>& m) const{
        size_t r = m.size();
        if(!r)return r;
        auto i=m.be;
        r^=hash<type(i)>()(i);
        ++i;
        r^=cbitl(hash<type(i)>()(*i),sizeof(r)*8/4);
        i=m.end();
        --i;
        r^=cbitl(hash<type(i)>()(*i),sizeof(r)*8/2);
        return r;
    }
};
template<>template<class A, class B>struct hash<pair<A,B>>{
    size_t operator()(const pair<A,B>& p) const{
        return hash<A>()(p.first) ^ cbitl(hash<B>()(p.second),sizeof(size_t)*8/2);
    }
};
}

#define rint _rint()
#define ruint _ruint()
#define rll _rll()
#define rull _rull()
#define rchar _rchar()

#ifndef FASTIO
inline void fin(int){}inline void fout(int){}
#ifdef IOSTREAM
inline int _rint(){int r;cin>>r;return r;}
inline uint _ruint(){uint r;cin>>r;return r;}
inline ull _rull(){ull r;cin>>r;return r;}
inline char _rchar(){return cin.get();}
template<typename T>inline void W(const T& i){cout<<i;}
inline void W(){W('\n');}
#else
inline int _rint(){int r;scanf("%d",&r);return r;}
inline uint _ruint(){uint r;scanf("%u",&r);return r;}
inline ull _rull(){ull r;scanf("%llu",&r);return r;}
inline ull _rll(){ll r;scanf("%lld",&r);return r;}
inline char _rchar(){return getchar();}
inline void W(char a='\n'){printf("%c",a);}
inline void W(int a){printf("%d",a);}
inline void W(uint a){printf("%u",a);}
inline void W(const ull& a){printf("%llu",a);}
inline void W(const ll& a){printf("%lld",a);}
inline void W(const char *str){fputs(str,stdout);}
inline void W(const double& d){printf("%.20f",d);}
inline void W(const long double& d){printf("%.50Lf",d);}
#endif
#else

#ifndef NO_UNLOCKED
#define FREAD fread_unlocked
#define FWRITE fwrite_unlocked
#else
#define FREAD fread
#define FWRITE fwrite
#endif

// todo: test on pointers
const int _IB=32768;const int _OB=32768;
char _iB[_IB];int _iP = _IB;char _oB[_OB];int _oP = 0;
inline void fin(int mc){int r=_IB-_iP;if(r>mc)return;fo(i,r)_iB[i]=_iB[i+_iP];	// TODO: memcpy
    FREAD(_iB+r,1,_iP,stdin);_iP = 0;}
inline void fout(int mc){if(_OB-_oP>mc)return;FWRITE(_oB,1,_oP,stdout);_oP = 0;}
inline void W(char c='\n'){_oB[_oP++]=c;}
inline char _rchar(){return _iB[_iP++];}
template<class T>inline T _rur(){
    T r=0;char c=rchar;
    do c-='0',r=r*10+c,c=rchar;while(c>='0');
    return r;}
template<class T>inline T _rsi(){
	char c=rchar;
	while(c<'-')c=rchar;
	if(c=='-')return -_rur<T>();
	else{--_iP;return _rur<T>();}}
template<class T>inline T _ru(){while(rchar<'0');--_iP;return _rur<T>();}

inline int _rint(){fin(15);return _rsi<int>();}
inline uint _ruint(){fin(15);return _ru<uint>();}
inline ll _rll(){fin(25);return _rsi<ll>();}
inline ull _rull(){fin(25);return _ru<ull>();}

const int _rs = 20;char _r[_rs];
template<class T>inline void _w(T i){
	if(numeric_limits<T>::is_signed && i<0)W('-'),i=-i;
	else if(i==0){W('0');return;}
	int pos = _rs;
	do{_r[--pos]='0'+i%10;i/=10;}while(i);
	do W(_r[pos]),++pos;while(pos<_rs);}
inline void W(const int32_t& i){fout(15);_w(i);}
inline void W(const uint32_t& i){fout(15);_w(i);}
inline void W(const int64_t& i){fout(25);_w(i);}
inline void W(const uint64_t& i){fout(25);_w(i);}
inline void W(const char*str){int l=strlen(str);fout(l);memcpy(&_oB[_oP],str,l);_oP+=l;}
inline void W(double d){fout(50);_oP+=sprintf(&_oB[_oP],"%.20f",d);}	// todo
#endif
template<class A,class B>inline void W(const A&a,const B&b){W(a);W(b);}
template<class A,class B,class C>
inline void W(const A&a,const B&b,const C&c){W(a);W(b);W(c);}
template<class A,class B,class C,class DD>
inline void W(const A&a,const B&b,const C&c,const DD&dd){W(a);W(b);W(c);W(dd);}
template<class T>inline void sortall(T&t){sort(t.be,t.en);}
template<class T>inline void uniqueall(T&t){t.resize(unique(t.be,t.en));}

inline int count1(uint i){return __builtin_popcount(i);}
inline int count1(ull i){return __builtin_popcountll(i);}
inline int parity(uint i){return __builtin_parity(i);}
inline int parity(ull i){return __builtin_parityll(i);}
inline int ilog(uint i){return 31-__builtin_clz(i);} // int log; floor(log2(i))
inline int ilog(ull i){return 63-__builtin_clzll(i);}
#define powerof2(x) !(x&(x-1))
#define subset(a,b) (a&b==a)
#define kbegin(k) ((1<<k)-1)
#define kend(k,n) ((kbegin(k)<<n-k)+1)
inline uint knext(uint a){uint b=(a|(a-1))+1;return b|((a^b)>>(__builtin_ctz(a)+2));}
#define fors(x,k,n) for(uint x=kbegin(k);x<kend(k,n);x=knext(x))


template<class A,class B>inline ostream&operator<<(ostream&o,const pair<A,B>&p){o<<'<'<<p.fi<<", "<<p.se<<'>';return o;}
template<class A,class B>inline ostream&operator<<(ostream&o,const map<A,B>&m){o<<N;for(auto&k:m)o<<"map["<<k.fi<<"] -> "<<k.se<<N;return o;}
template<class A>inline ostream&operator<<(ostream&o,const vector<A>&v){o<<N;fo(i,v.sz)o<<"vector["<<i<<"] = "<<v[i]<<N;return o;}

struct _O{template<class T>_O&operator<<(const T&t){oc(1);W(t);oc(0);return*this;}}O;
struct _I{
	_I&operator>>(int32_t&t){t=rint;return*this;}
	_I&operator>>(uint32_t&t){t=ruint;return*this;}
	_I&operator>>(int64_t&t){t=rll;return*this;}
	_I&operator>>(uint64_t&t){t=rull;return*this;}
}I;

struct _E{template<class T>_E&operator<<(const T&t){D{ec(1);cerr<<t;ec(0);}return*this;}}E;



inline void tc();
int main()
{
#ifdef FASTIO
    setvbuf(stdin,0,_IONBF,0);setvbuf(stdout,0,_IONBF,0);
#elif defined IOSTREAM
	ios_base::sync_with_stdio(0);cin.tie(0);cout.precision(99);cout.setf(ios::fixed,ios::floatfield);
#endif

#ifdef DEBUG
#ifdef _WIN32
	ec(0);
	oc(0);
#else
// TODO: *nix
#endif
#endif
	
#ifdef READ_NUM_TEST_CASES
	int nz=rint;fo(i,nz)
#endif
	tc();
#ifdef FASTIO
    FWRITE(_oB,1,_oP,stdout);
#endif
	return 0;
}
// END OF TEMPLATE














#include<type_traits>

namespace ab
{


template<bool cond, typename T, typename F> struct IF {typedef T R;};
template<typename T, typename F> struct IF<false,T,F> {typedef F R;};

template <bool B, class T = void> struct ENABLE_IF {typedef T R;};
template <class T> struct ENABLE_IF<false, T> {};

template <bool B, class T = void> struct DISABLE_IF {typedef T RET;};
template <class T> struct DISABLE_IF<true, T> {};



template<typename A, typename B>
struct SAME_TYPE
{
	static const bool RET = false;
};
template<typename T>
struct SAME_TYPE<T,T>
{
	static const bool RET = true;
};


template<typename T>
struct IS_CLASS
{
	template<typename C> static char (&f(int C::*))[1];
	template<typename C> static char (&f(...))[2];

	static bool const R = sizeof(f<T>(0))==1;
};



struct FALSE
{
	static bool const R = false;
};

template<class T>
struct RR{
typedef typename std::remove_reference<T>::type R;
};


// get &T::x or &T::first
template<class T,class=void>struct GET_X{};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::x)>::value>::type>{typedef decltype(&T::x) R;};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::first)>::value>::type>{typedef decltype(&T::first) R;};

// get &T::y or &T::second
template<class T,class=void>struct GET_Y{};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::y)>::value>::type>{typedef decltype(&T::y) R;};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::second)>::value>::type>{typedef decltype(&T::second) R;};






}


namespace ab{

/////////////////////////////// STATIC ARRAY ///////////////////////////////////
// requires: TEMPLATES
//
// Copyright (c) 2013 by Adam Blaszkiewicz. All rights reserved.
//
template<typename T, int _capacity>
class StaticArray
{
public:
	StaticArray() : mSize(0) {}
	StaticArray(unsigned int _size) : mSize(_size) {A(_size<=_capacity);}
	inline void push_back(const T& t) {new(&mData()[mSize]) T(t); ++mSize;}
	inline void push_back() {new(&mData()[mSize]) T; ++mSize;}
	inline void pop_back() {A(mSize>0); --mSize; mData()[mSize].~T();}
	inline T& operator[](const int idx) {return mData()[idx];}
	inline const T& operator[](const int idx) const {A(idx<mSize); return mData()[idx];}
	inline T& back() {A(mSize>0); return mData()[mSize-1];}
	inline const T& back() const {A(mSize>0); return mData()[mSize-1];}
	inline T& front() {A(mSize>0); return mData()[0];}
	inline const T& front() const {A(mSize>0); return mData()[0];}
	inline int size() const {return mSize;}
	inline unsigned int capacity() const {return _capacity;}
	inline void resize(int newSize)
	{
		A(newSize <= _capacity);
		if(newSize > mSize) new (&mData()[mSize]) T[newSize-mSize];
		else for(int i=newSize; i<mSize; ++i) mData()[i].~T();
		mSize = newSize;
	}
	inline void reserve(int howMuch) const {A(howMuch <= _capacity);}
	inline void clear() {for(int i=0; i<mSize; ++i) mData()[i].~T(); mSize=0;}
	typedef T* iterator;
	inline iterator begin() {return mData;}
	inline iterator end()   {return mData+mSize;}
private:
	T* mData() {return reinterpret_cast<T*>(_mData);}
	char _mData[_capacity*sizeof(T)];
	int mSize;
};

// vector of at most n elements
template<typename T, int n> struct _vector
{typedef typename IF<n==0,std::vector<T>,StaticArray<T,n> >::R R;};
////////////////////////////////////////////////////////////////////////////////

}


namespace ab{


////////////////////////////////////////////////////////////////////////////////
///////////////////////////////// GRAFY ////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////






////////////////////////////////////////////////////////////////////////////////
// BINDER
template<typename Ret, typename T>
class Binder
{
public:
	Binder(Ret T::*_var) : var(_var) {}
	Ret& operator()(T& obj) const
	{
		return obj.*var;
	}
	const Ret& operator()(const T& obj) const
	{
		return obj.*var;
	}
private:
	Ret T::*var;
};
template<typename Ret, typename T>
Binder<Ret,T> bind(Ret T::*var)
{
	return Binder<Ret,T>(var);
}
////////////////////////////////////////////////////////////////////////////////






////////////////////////////////////////////////////////////////////////////////
// KLASY GRAFOW //
// * wska┼║niki (PE, PV) i iteratory nie mog─ů du┼╝o zajmowa─ç,
//   bo mog─ů by─ç pami─Ötane przez np. Dinica
// * Dlatego s─ů to prawie (ca┼ékiem?) go┼ée wska┼║niki, kt├│re nie zawsze pozwalaj─ů
//   na wykonanie ┼╝─ůdanej operacji na tym, na co wskazuj─ů, np. usuwania kraw─Ödzi
// * Po to s─ů klasy VC i EC (context), kt├│re pozwalaj─ů wykonywa─ç
//   wszystkie dost─Öpne operacje
/*

template<uint _NMax = 0, uint _MMax = 0, typename _VExtra = VOID, typename _EExtra = VOID>
class G
{
public:
	static const uint NMax = _NMax;
	static const uint MMax = _MMax;
	typename _VExtra VExtra;
	typename _EExtra EExtra;

	struct VC//ontext
	{
		struct TO<E>
		{
			struct iterator : public PE
			{
				// ...
			};
			iterator begin();
			iterator end();

			EContext operator[](PE&);
		} to;
	};
	}

	struct EC//ontext
	{
		EExtra& operator->()
		VContext fr();
		VContext to();
		EContext rev() const;		// rev must be enabled
		bool revEnabled() const;
		void erase();
		void disable();				// EC becomes invalid
		void enableRev();			// rev must be disabled
	}


	struct PE;

	struct VS<V>
	{
		struct iterator : public PV
		{
			// ...
		};
		iterator begin();
		iterator end();

		VContext operator[](PV&);
	} vs;

	struct ES<E>
	{
		struct iterator : public PE
		{
			// ...
		};
		iterator begin();
		iterator end();

		EContext operator[](PE&);
	} es;

	struct V : public VExtra
	{
		V(VContext);
	};
	struct E : public EExtra
	{
		E(EContext);
	};
};
*/
////////////////////////////////////////////////////////////////////////////////




////////////////////////////////////////////////////////////////////////////////
// 2014-05-12
//              Vs			Es
// Iterate		no			yes
// Erase		no			no
// point		int			pointer
// rev						no
//
// Avoid vs reallocation! (?)
//
// Good for: Kruskal
//
// dummy vertices
//
template<typename VExtra=VOID, typename EExtra=VOID, uint NMax=0, uint MMax=0> class GraphU_EI{};
template<typename _EExtra, uint _NMax, uint _MMax>
class GraphU_EI<VOID,_EExtra,_NMax,_MMax>	// edges iterable
{
private:
	class V; class E;
	
public:
	static const uint NMax = _NMax;
	static const uint MMax = _MMax;
	typedef VOID VExtra;
	typedef _EExtra EExtra;
	typedef uint PV; typedef E* PE;
	
private:
	class V : public VExtra{
	};
	class E : public EExtra{
		friend class GraphU_EI;
		E(const PV& _fr, const PV& _to, const EExtra& eExtra) : EExtra(eExtra), fr(_fr), to(_to) {}
		PV fr,to;
	};
	
public:
	class VC; class EC; class VS; class ES;
	
	class VC{
	public:
		VC(GraphU_EI&_g, const PV& _v) : g(_g), v(_v){}
		operator PV()const{return v;}
	private:
		GraphU_EI& g;
		PV v;
	};
	class EC{
	public:
		EExtra* operator->(){return e;}
		template<class T> decltype(PE()->*T()) operator->*(const T& t){return e->*t;}
		operator PE()const{return e;}
		VC fr(){return VC(g,e->fr);}
		VC to(){return VC(g,e->to);}
		void fr(const PV& _fr){e->fr=_fr;}
		void to(const PV& _to){e->to=_to;}
		EC(GraphU_EI&_g, const PE& _e) : g(_g), e(_e) {}
	private:
		GraphU_EI& g;
		PE e;
	};
	
	class VS{
		friend class GraphU_EI;
	public:
		typedef uint iterator;
		uint size()const{return g.vsSize;}
		void resize(uint _size){g.vsSize=_size;}
		iterator begin()const{return 0;}
		iterator end()const{return g.vsSize;}
	private:
		GraphU_EI& g;
		VS(GraphU_EI& _g) : g(_g) {}
	} vs;
	
	class ES{
		friend class GraphU_EI;
	public:
		typedef PE iterator;
		inline iterator begin() {return &*g._es.begin();}
		inline iterator end()   {return &*g._es.end();}
		
		inline uint size()const{return g._es.size();}
		inline void resize(unsigned int _size) {g._es.resize(_size);}
		inline void reserve(unsigned int _size) {g._es.reserve(_size);}
		
		inline void push_back(const PV& from, const PV& to, const EExtra& eExtra = EExtra()){
			g._es.push_back(E(from,to,eExtra));
		}

		inline EC operator[](const PE& pe) {return EC(g,pe);}
		inline EC operator[](unsigned int idx){
			A(MMax==0 || idx < MMax);
			return EC(g,&g._es[idx]);
		}
	private:
		GraphU_EI& g;
		ES(GraphU_EI& _g) : g(_g) {}
	} es;
	
	GraphU_EI() : vs(*this), es(*this), vsSize(0) {}
	
private:
	typedef typename _vector<E,NMax>::R _ES;
	_ES _es;
	uint vsSize;
};




////////////////////////////////////////////////////////////////////////////////
// 2013-11-15
//              Vs			Es
// Iterate		yes			no
// Erase		no			yes
// point		pointer		pointer
// rev						yes
//
// Avoid vs reallocation!
// Es paired or single
//
// Good for: Dinic
//
// use BaseG::VExtra
// otherwise use G
template<typename _VExtra = VOID, typename _EExtra = VOID, uint _NMax = 0, uint _MMax = 0>
class BaseGraphU_ERD
{
public:
	static const uint NMax = _NMax;
	static const uint MMax = _MMax;
	typedef _VExtra VExtra;
	typedef _EExtra EExtra;

private:
	class V; class E;

public:
	typedef V* PV;
	typedef E* PE;

	typedef typename _vector<V,NMax>::R _VS;
public:
	inline BaseGraphU_ERD(_VS& __vs) : _vs(__vs), vs(*this) {}
	_VS& _vs;
private:
	struct E : public EExtra
	{
		inline E(const PV& _to, const PE& _rev, const EExtra& ee = EExtra()) :
			EExtra(ee), to(_to), rev(_rev) {}
		inline E(const E& o) : EExtra(o), to(o.to), rev(o.rev)
		{
			if(rev) rev->rev = this;
		}
		inline E& operator=(const E& o)
		{
			EExtra::operator=(o);
			to = o.to;
			rev = o.rev;
			if(rev) rev->rev = this;
			return *this;
		}
		PV to;
		PE rev;
	};

	class V : public VExtra
	{
		friend class BaseGraphU_ERD;
	private:
		std::vector<E> to;
	};

	//_VS& _vs;


public:
	class VC; class EC; class VS;

	class VC//ontext
	{
		friend class VS;
		friend class EC;
	public:
		struct TO
		{
			friend class BaseGraphU_ERD;
		private:
			BaseGraphU_ERD& g;
			PV pv;
			inline TO(BaseGraphU_ERD& _g, PV& _pv) : g(_g), pv(_pv) {}
			inline void push_back(const E& e)
			{
				pv->to.push_back(e);
			}
		public:
			typedef PE iterator;
			inline iterator begin() {return &*pv->to.begin();}
			inline iterator end()   {return &*pv->to.end();}
			inline void reserve(unsigned int size) {pv->to.reserve(size);}
			inline E& back() {return pv->to.back();}
			inline const E& back() const {return pv->to.back();}
			inline E& front() {return pv->to.front();}
			inline const E& front() const {return pv->to.front();}

			inline EC operator[](PE& pe)
			{
				return EC(g,pe,pv);
			}
		} to;

		inline V& operator*() {return *to.pv;}
		inline const V& operator*() const {return *to.pv;}
		inline V* operator->() {return to.pv;}
		inline const V* operator->() const {return to.pv;}
		inline operator PV() const {return to.pv;}
	private:
		inline VC(BaseGraphU_ERD& _g, PV _pv) : to(_g,_pv) {}
	};


	class EC//ontext
	{
		friend class VC::TO;
	public:
		inline VC to() const {return VC(g,pe->to);}
		inline EC rev() const {return EC(g,pe->rev,pe->to);}		// rev must be enabled
		inline bool revEnabled() const {return pe->rev != 0;}
		inline void delSingle()
		{
			A(!pe->rev);	// single
			g._delE(pvfrom,pe);
		}
		inline void delPaired()
		{
			g._delE(pe->to, pe->rev);
			g._delE(pvfrom, pe);
		}
		inline void del()	// !!! SLOWER !!!
		{
			if(pe->rev) _delE(pe->to, pe->rev);
			g._delE(pvfrom, pe);
		}
		inline void disable()	// EC becomes invalid, rev must be enabled
		{
			PE reve = pe->rev;
			g._delE(pvfrom, pe);
			reve->rev = 0;
		}
		inline void enableRev()	// rev must be disabled
		{
			A(pe->rev==0);
			pe->rev = &*pe->to->to.begin() + pe->to->to.size();
			pe->to->to.push_back(E(pvfrom,pe));
		}

		inline operator PE() const {return pe;}
	private:
		inline EC(BaseGraphU_ERD& _g, const PE& _pe, const PV& _pvfrom) :
			g(_g), pe(_pe), pvfrom(_pvfrom) {}
		BaseGraphU_ERD& g;
		PE pe;
		PV pvfrom;
	};

	class VS
	{
		friend class BaseGraphU_ERD;
	public:
		typedef PV iterator;
		inline iterator begin() {return &*g._vs.begin();}
		inline iterator end()   {return &*g._vs.end();}

		inline void resize(unsigned int size) {g._vs.resize(size);}

		inline VC operator[](const PV& pv) {return VC(g,pv);}
		inline VC operator[](unsigned int idx)
		{
			A(NMax==0 || idx < NMax);
			return VC(g,&g._vs[idx]);
		}
	private:
		BaseGraphU_ERD& g;
		VS(BaseGraphU_ERD& _g) : g(_g) {}
	} vs;

	inline void addSingle(PV vot, PV vto, EExtra extra = EExtra())
	{
		vot->to.push_back(E(vto,0,extra));
	}

	inline void addPaired(const PV& vot, const PV& vto, const EExtra& extra1 = EExtra(), const EExtra& extra2 = EExtra())
	{
		vot->to.push_back(E(vto,0,extra1));
		vto->to.push_back(E(vot,0,extra2));
		vot->to.back().rev = &*vto->to.begin()+vto->to.size()-1;
		vto->to.back().rev = &*vot->to.begin()+vot->to.size()-1;
		/*
		vs[vot].to.push_back();
		E& e1 = vs[vot].to.back();
		vs[vto].to.push_back();
		E& e2 = vs[vto].to.back();
		e1.~E();	// avoid copy constructors
		new(&e1) E(vto, &e2, extra1);
		e2.~E();
		new(&e2) E(vot, &e1, extra2);*/
	}
private:
	inline void _delE(const PV& pvfrom, const PE& pe)
	{
		*pe = pvfrom->to.back();
		pvfrom->to.pop_back();
	}
};
template<typename _VExtra = VOID, typename _EExtra = VOID, uint _NMax = 0, uint _MMax = 0>
class GraphU_ERD	// edges removable, disableable
	: public BaseGraphU_ERD<_VExtra,_EExtra,_NMax,_MMax>//raphU_ERD
{
public:
	typedef BaseGraphU_ERD<_VExtra,_EExtra,_NMax,_MMax> BASE;
	inline GraphU_ERD() : BASE(__vs) {}
	typename BASE::_VS __vs;
};
////////////////////////////////////////////////////////////////////////////////





}




#include<cstring>
#include<vector>

namespace ab{

////////////////////////////////// UNION FIND //////////////////////////////////
class UnionFind
{
public:
	UnionFind(size_t univSize) : parents(univSize), ranks(univSize,0)
	{
		for(size_t i=0; i<univSize; ++i) parents[i] = i;
	}
	size_t find(size_t x)
	{
		size_t root = x;
		while(parents[root] != root) root = parents[root];
		while(x != root)
		{
			size_t& curr = parents[x];
			x = parents[x];
			curr = root;
		}
		return root;
	}
	bool makeUnion(size_t a, size_t b) // false if union already made
	{
		a = find(a);
		b = find(b);
		if(a==b)return false;
		if(ranks[a] < ranks[b]) parents[a] = b, ++ranks[b];
		else parents[b] = a, ++ranks[a];
		return true;
	}
private:
	std::vector<size_t> parents;
	std::vector<size_t> ranks;
};
////////////////////////////////////////////////////////////////////////////////

}


namespace ab
{
	// MST
	// O(m log n)
	//
	// minNumComponents is optional, for optimization; setting lower than actual number of components is ok
	//
	// zeroResult=false wydaje sie nic nie przyspieszac
	//
	// sorted=true znacznie przyspiesza. mo┐na u┐yŠ counting sorta wczesniej
	//
	#ifdef OLD_COMPILER
	template<typename G, typename EWeight, typename EResult, bool sorted = false, bool zeroResult=true, int minNumComponents = 1>
	#else
	template<bool sorted = false, bool zeroResult=true, int minNumComponents = 1, typename G, typename EWeight, typename EResult>
	#endif
	int kruskal(G& g, const EWeight& eWeight, const EResult& eResult)
	{
		unsigned int numEdges = g.es.size();
		unsigned int numVerts = g.vs.size();
		
		if(!sorted)std::sort(g.es.begin(),g.es.end(),[eWeight](const typename G::EExtra& a, const typename G::EExtra& b){return a.*eWeight < b.*eWeight;});
		
		UnionFind uf(numVerts);
		int numFound = 0;
		
		int i=0;
		for(; i<numEdges && numFound < numVerts-minNumComponents; ++i)
		{
			typename G::PV a = g.es[i].fr();
			typename G::PV b = g.es[i].to();
			int aa = uf.find(a-g.vs.begin());
			int bb = uf.find(b-g.vs.begin());
			if(aa==bb){
				if(zeroResult)g.es[i]->*eResult = false;
				continue;
			}
			
			uf.makeUnion(aa,bb);
			++numFound;
			g.es[i]->*eResult = true;
		}
		if(zeroResult) for(;i<numEdges;++i) g.es[i]->*eResult = false;
		
		return numFound;
	}
	
	#ifdef OLD_COMPILER
	template<typename G, typename EWeight, bool sorted = false, unsigned int minNumComponents = 1>
	#else
	template<bool sorted = false, unsigned int minNumComponents = 1, typename G, typename EWeight>
	#endif
	std::vector<typename G::PE> kruskal(G& g, const EWeight& eWeight)
	{
		unsigned int numEdges = g.es.size();
		unsigned int numVerts = g.vs.size();
		
		if(!sorted)std::sort(g.es.begin(),g.es.end(),[eWeight](const typename G::EExtra& a, const typename G::EExtra& b){return a.*eWeight < b.*eWeight;});
		
		UnionFind uf(numVerts);
		std::vector<typename G::PE> result;
		result.reserve(numVerts-minNumComponents);
		
		for(int i=0; i<numEdges && result.size() < numVerts-minNumComponents; ++i)
		{
			typename G::PV a = g.es[i].fr();
			typename G::PV b = g.es[i].to();
			int aa = uf.find(a-g.vs.begin());
			int bb = uf.find(b-g.vs.begin());
			if(aa==bb)continue;
			
			uf.makeUnion(aa,bb);
			result.push_back(g.es[i]);
		}
		
		return result;
	}
	
	
	template<typename Weight>
	struct _boruvkaCleanupEdge
	{
		int from;
		int to;
		Weight val;
		int orig;
		
		static int getFrom(const _boruvkaCleanupEdge& e)
		{
			return e.from;
		}
		static int getTo(const _boruvkaCleanupEdge& e)
		{
			return e.to;
		}
	};
	/*
	// MST
	// sets resultEDataKey to true for edges in MST, does not set resultEDataKey for other edges
	// O(min(m log n, n^2))
	// O(n) if planar
	// set cleanupfirst = false if there are no multiple (u,v) edges
	// Old paper by Cheriton, ...
	template<bool cleanupFirst = true, typename G, typename EWeight>
	std::vector<G::PE> boruvkaCleanup(G& g, const EWeight& eWeight)
	{
		int numTrees = g.vs.size();
		
		std::vector<_boruvkaCleanupEdge<Weight>> edges(g.edges.size());
		for(unsigned int i=0; i<g.edges.size(); ++i)
		{
			edges[i].from = g.edges[i].from;
			edges[i].to   = g.edges[i].to;
			edges[i].val  = getWeightEData(g.edges[i]);
			edges[i].orig = i;
		}
		
		std::pair<int,Weight> *bests = new std::pair<int,Weight>[numTrees];
		int *vmap = new int[numTrees];
		
		int numFound = 0;
		
		for(;;)
		{
			// cleanup
			if(numFound != 0 || cleanupFirst)
			{
				std::vector<_boruvkaCleanupEdge<Weight> > helperEdges(edges.size());
				countingSort(&edges[0], &edges[0] + edges.size(), &helperEdges[0], numTrees, _boruvkaCleanupEdge<Weight>::getTo);
				countingSort(&helperEdges[0], &helperEdges[0] + edges.size(), &edges[0], numTrees, _boruvkaCleanupEdge<Weight>::getFrom);
				int curDest = 0;
				int prev1 = -1;
				int prev2 = -1;
				Weight bestval = 0;
				int bestarg = 0;
				//printf("edges size %d\n", edges.size());
				for(unsigned int i=0; i<edges.size(); ++i)
				{
					int n1 = edges[i].from;
					int n2 = edges[i].to;
					
					if(n1 == n2) continue;
					
					if(prev1 == n1 && prev2 == n2)
					{
						if(edges[i].val < bestval) bestval = edges[i].val, bestarg = i;
					}
					else
					{
						if(prev1 != -1) edges[curDest++] = edges[bestarg];
						bestval = edges[i].val;
						bestarg = i;
						prev1 = n1;
						prev2 = n2;
					}
				}
				if(prev1 != -1) edges[curDest++] = edges[bestarg];
				edges.resize(curDest);
			}
			//cleanup end
			
			//printf("Cheriton step: %d trees, %d edges, found %d\n",numTrees,edges.size(),numFound);
			
			// find bests
			memset(bests, 0xff, sizeof(std::pair<int,Weight>)*numTrees);
			for(unsigned int i=0; i<edges.size(); ++i)
			{
				//printf("%x\n",bests[a].first);
				int a = edges[i].from;
				if((unsigned int)bests[a].first == 0xffffffff || bests[a].second > edges[i].val)
				{
					bests[a].second = edges[i].val;
					bests[a].first = i;
				}
				
				int b = edges[i].to;
				if((unsigned int)bests[b].first == 0xffffffff || bests[b].second > edges[i].val)
				{
					bests[b].second = edges[i].val;
					bests[b].first = i;
				}
			}
			// find bests end
		
			UnionFind uf(numTrees);
			bool change = false;
			for(int i=0; i<numTrees; ++i)
			{
				int best = bests[i].first;
				if((unsigned int)best == 0xffffffff) continue;
				
				int a = edges[best].from;
				int b = edges[best].to;
				a = uf.find(a);
				b = uf.find(b);
				if(a==b)continue;
				
				uf.makeUnion(a,b);
				getResultEData(g.edges[edges[best].orig]) = true;
				++numFound;
				change = true;
			}
			
			if(!change) break;
			
			// przemianowanie
			int newNumTrees = 0;
			memset(vmap, 0xff, sizeof(int)*numTrees);
			for(int i=0; i<numTrees; ++i)
			{
				int a = uf.find(i);
				if((unsigned int)vmap[a] == 0xffffffff) vmap[a] = newNumTrees++;
				vmap[i] = vmap[a];
			}
			for(unsigned int i=0; i<edges.size(); ++i)
			{
				edges[i].from = vmap[edges[i].from];
				edges[i].to   = vmap[edges[i].to];
			}
			numTrees = newNumTrees;
			// przemianowanie end
		}
		
		delete[] bests;
		delete[] vmap;
		return numFound;
	}
	*/
}


struct EExtra{
	int weight;
};
typedef GraphU_EI<VOID,EExtra> G;

inline void tc()
{
	uint n;
	I>>n;
	
	G g;
	g.vs.resize(n+1);
	g.es.reserve(n*(n+1)/2);
	fo(i,n)fo(j,i+1,n+1){
		int val = rint;
		g.es.pub(i,j,EExtra{val});
	}
	
	auto result = kruskal(g,&EExtra::weight);
	A(result.sz+1 == n);	// tree
	
	ui64 r = 0;
	fo(i,result.sz)r += result[i]->weight;
	
	O<<r<<N;
}