//#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

#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 puf push_front
#define pob pop_back()
#define pof pop_front()
#define bs binary_search
#define lb lower_bound
#define ub upper_bound

#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))



#ifdef OLD_COMPILER
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
#include<string>
#include<stdint.h>
#include<cstring>
#include<iostream>
#else
#include<bits/stdc++.h>
#endif





#ifdef OLD_COMPILER

#else
#include<cstdint>
#endif

#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."
#undef FASTIO

#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>



#ifdef OLD_COMPILER
// TODO
#else
#include<type_traits>
#endif


#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(__typeof((c).begin())e=(c).begin();e!=(c).end();++e)


#define MIN_GCC(a,b,c) (__GNUC__ > (a) || \
              (__GNUC__ == (a) && (__GNUC_MINOR__ > (b) || \
                                 (__GNUC_MINOR__ == (b) && \
                                  __GNUC_PATCHLEVEL__ >= (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

#define all(x) (x).be,(x).en
#define type(x) __typeof(x)

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{




#if defined __GNUC__ and not MIN_GCC(4,2,0)
template<class T>struct hash<T>{}
#endif

// 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 uniqall(T&t){t.resize(unique(t.be,t.en)-t.be);}

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













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{


//////////////////////// SPLAYER (for splay trees) /////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2013-2014
//
/*
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
//
// Splayer provides some splay node operations
template<bool evertable = false>
struct Splayer
{
	template<typename PV>
	static inline void updateUntilNode(PV x, const PV& superRoot)
	{
		while(x != superRoot)
		{
			A(x);
			x->template update<0,0>();
			x = x->parent;
		}
	}
	template<typename SplayNode>
	static inline void updateUntilNull(SplayNode* x)
	{
		updateUntilNode(x,NULL);
	}
	template<typename SplayNode>
	static inline void splayUntilNode(SplayNode *x,
		const SplayNode* const superRoot, int level)
	{
		//int level = 0;
		//SplayNode *pc = x;
		//while(pc->parent != superRoot()) pc = pc->parent, ++level;
		int level2 = level/2;
		while(level2) splay(x),--level2;
		if(level&1) rotate(x);
		A(x->parent == superRoot);
	}
	template<typename SplayNode>
	static inline void splayUntilNode(SplayNode *x, SplayNode *superRoot)
	{
		int level = 0;
		SplayNode *pc = x;
		while(pc->parent != superRoot) pc = pc->parent, ++level;
		splayUntilNode(x,superRoot,level);
	}
	template<typename SplayNode>
	static inline void splayUntilNull(SplayNode *x, int level)
	{
		if(level==0)return;
		if(level==1)rotateLast(x);
		else
		{
			int level2 = level/2;
			while(--level2) splay(x);
			if(level&1) splay(x),rotateLast(x);
			else splayLast(x);
		}
		A(x->parent == NULL);
	}
	// returns previous root
	template<typename SplayNode>
	static inline SplayNode* splayUntilNull(SplayNode *x)
	{
		int level = 0;
		SplayNode *pc = x;
		while(pc->parent) pc = pc->parent, ++level;
		splayUntilNull(x,level);
		return pc;
	}

	// splay only right
	template<typename SplayNode>
	static inline void splayRUntilNull(SplayNode *x, int level)
	{
		if(level==0)return;
		if(level==1)rotateRLast(x);
		else
		{
			int level2 = level/2;
			while(--level2) rotateR(x->parent),rotateR(x);
			if(level&1) rotateR(x->parent),rotateR(x),rotateRLast(x);
			else rotateRLast(x->parent),rotateRLast(x);
		}
		A(x->parent == NULL);
	}
	// returns previous root
	template<typename SplayNode>
	static inline SplayNode* splayRUntilNull(SplayNode *x)
	{
		int level = 0;
		SplayNode *pc = x;
		while(pc->parent) pc = pc->parent, ++level;
		splayRUntilNull(x,level);	// bugfix
		return pc;
	}


	// ROTATIONS

	// assumes x's parent is NOT root (its parent != NULL)
	template<typename SplayNode>
	static inline void rotateR(SplayNode* x)
	{
		A(x->parent && x->parent->parent);
		SplayNode *prevParent = rotateRLast(x);
		A(x->parent);
		if(x->parent->l == prevParent) x->parent->l = x;
		else {A(x->parent->r == prevParent); x->parent->r = x;}
	}
	// assumes x's parent is root (its parent == NULL)
	// return prev parent
	template<typename SplayNode>
	static inline SplayNode* rotateRLast(SplayNode* x)
	{
		A(x); A(x->parent);
		A(x->parent->l == x);	// can rotate right
		SplayNode *parent = x->parent;
		SplayNode* xr;
		if(evertable && x->getSwapFlag())
		{
			xr = x->l;
			x->l = x->r;
			if(x->l) x->l->setSwapFlag(!x->l->getSwapFlag());
			if(xr) xr->setSwapFlag(!xr->getSwapFlag());
		}
		else
		{
			xr = x->r;
		}
		parent->l = xr;
		//parent->subVal(x);
		//parent->addVal(xr);
		//x->subVal(xr);
		//x->addVal(parent);
		
		//x->updateCopy(parent);
		if(xr)
		{
			xr->parent = parent;
			parent->template update<1,0>();	// L
		}
		else parent->template update<-1,0>();	// NL
		x->parent = parent->parent;
		x->setSwapFlag(parent->getSwapFlag());
		parent->setSwapFlag(false);
		x->r = parent;
		parent->parent = x;
		x->template update<0,1>();
		return parent;
	}
	// assumes x's parent is NOT root (its parent != NULL)
	template<typename SplayNode>
	static inline void rotateL(SplayNode* x)
	{
		A(x->parent->parent);
		SplayNode *prevParent = rotateLLast(x);
		if(x->parent->l == prevParent) x->parent->l = x;
		else {A(x->parent->r == prevParent); x->parent->r = x;}
	}
	// assumes x's parent is root (its parent == NULL)
	// returns prev parent
	template<typename SplayNode>
	static inline SplayNode* rotateLLast(SplayNode* x)
	{
		A(x); A(x->parent);
		A(x->parent->r == x);	// can rotate left
		SplayNode *parent = x->parent;
		SplayNode *xl;
		if(evertable && x->getSwapFlag())
		{
			xl = x->r;
			x->r = x->l;
			if(x->r) x->r->setSwapFlag(!x->r->getSwapFlag());
			if(xl) xl->setSwapFlag(!xl->getSwapFlag());
		}
		else
		{
			xl = x->l;
		}
		parent->r = xl;
		//parent->subVal(x);
		//parent->addVal(xl);
		//x->subVal(xl);
		//x->addVal(parent);
		//x->updateCopy(parent);
		if(xl)
		{
			xl->parent = x->parent;
			parent->template update<0,1>();	// R
		}
		else parent->template update<0,-1>(); // NR
		x->parent = parent->parent;
		x->setSwapFlag(parent->getSwapFlag());
		parent->setSwapFlag(false);
		x->l = parent;
		parent->parent = x;
		x->template update<1,0>();
		return parent;
	}
	// assumes x's parent is NOT root (its parent != null)
	template<typename SplayNode>
	static inline void rotate(SplayNode* x)
	{
		A(x); A(x->parent); A(x->parent->parent);
		if(x->parent->r == x) rotateL(x);
		else {A(x->parent->l == x); rotateR(x);}
	}
	// assumes x's parent is root (its parent == null)
	template<typename SplayNode>
	static inline void rotateLast(SplayNode* x)
	{
		A(x); A(x->parent);A(!x->parent->parent);
		if(x->parent->r == x) rotateLLast(x);
		else {A(x->parent->l == x); rotateRLast(x);}
	}

	// assumes x's grandparent is NOT root (its parent != NULL)
	template<typename SplayNode>	// TODO: can be optimized if splays aren't
									// done using rotate functions but directly
	static inline void splay(SplayNode *x)	// zig-zig or zig-zag
	{
		A(x); A(x->parent); // x not root
		A(x->parent->parent); // parent not root
		A(x->parent->parent->parent); // there is superRoot
		SplayNode *p = x->parent;
		SplayNode *g = p->parent;
		if(evertable && p->getSwapFlag())
		{
			if(p->l == x)
			{
				if(g->l == p) rotateR(x), rotateR(x);
				else {A(g->r == p); rotateL(p), rotateL(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateR(p), rotateR(x);
				else {A(g->r == p); rotateL(x), rotateL(x);}
			}
		}
		else
		{
			if(p->l == x)
			{
				if(g->l == p) rotateR(p), rotateR(x);
				else {A(g->r == p); rotateR(x), rotateL(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateL(x), rotateR(x);
				else {A(g->r == p); rotateL(p), rotateL(x);}
			}
		}
	}

	// assumes x's grandparent is root (its parent == NULL)
	template<typename SplayNode>
	static inline void splayLast(SplayNode *x)	// zig-zig or zig-zag
	{
		A(x); A(x->parent); // x not root
		A(x->parent->parent); // parent not root
		SplayNode *p = x->parent;
		SplayNode *g = p->parent;
		if(evertable && p->getSwapFlag())
		{
			if(p->l == x)
			{
				if(g->l == p) rotateR(x), rotateRLast(x);
				else {A(g->r == p); rotateLLast(p), rotateLLast(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateRLast(p), rotateRLast(x);
				else {A(g->r == p); rotateL(x), rotateLLast(x);}
			}
		}
		else
		{
			if(p->l == x)
			{
				if(g->l == p) rotateRLast(p), rotateRLast(x);
				else {A(g->r == p); rotateR(x), rotateLLast(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateL(x), rotateRLast(x);
				else {A(g->r == p); rotateLLast(p), rotateLLast(x);}
			}
		}
	}
	// debug
	template<typename SplayNode>
	static inline bool consistent(const SplayNode *pv)
	{
		// parent link
		if(pv->parent && pv->parent->l!=pv && pv->parent->r!=pv) return false;
		// left link
		if(pv->l && pv->l->parent!=pv) return false;
		// right link
		if(pv->r && pv->r->parent!=pv) return false;
		// children are the same
		if(pv->l && pv->l == pv->r) return false;
		if(pv->l && pv->l == pv->parent) return false;
		if(pv->r && pv->r == pv->parent) return false;
		return true;
	}
};
////////////////////////////////////////////////////////////////////////////////



}


namespace ab{


////////////////////////// SPLAY NODES /////////////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2013-2014
//
/*
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
//
template<typename _Value, typename Derived> struct BaseSplayNode
{
	// Only data, should be no vptr
	_Value keyval;
	Derived *parent;
	Derived *l;
	Derived *r;

	// Children-less initialization
	inline BaseSplayNode(const _Value& _keyval, Derived* _parent) :
		keyval(_keyval), parent(_parent), l(NULL), r(NULL) {}

	// Full initialization
	inline BaseSplayNode(const _Value& _keyval, Derived* _parent, Derived* _l, Derived* __r) :
		keyval(_keyval), parent(_parent), l(_l), r(__r) {}

	// PATH AGGREGATION
	// "pure virtual" update functions
	inline void update() {A(false);}
	inline void updateLR() {A(l && r);A(false);}
	inline void updateL() {A(l);A(false);}
	inline void updateR() {A(r);A(false);}
	inline void updateNL() {A(!l);A(false);}
	inline void updateNR() {A(!r);A(false);}
	inline void updateCopy(Derived* x) {A(false);}	// copy stats from x

	// TODO: path aggregation for linear values - could be faster,
	//   especially when updating ancestors of deleted node

	// swap flag - for evert (rerooting)
	inline bool getSwapFlag() const {A(false); return 0;}
	inline void setSwapFlag(bool) {A(false);}

	// TREE AGGREGATION (only linear values)
	// suitable for sum, not suitable for max
	inline void addVal(Derived* x) {A(false);}
	inline void subVal(Derived* x) {A(false);}
};
template<typename _Value, typename Derived> struct CopyableSplayNode :
	public BaseSplayNode<_Value, Derived>
{
	typedef BaseSplayNode<_Value,Derived> B;//ASE
	inline void operator=(const CopyableSplayNode& o)
	{
		B::keyval = o.keyval;
		B::parent = o.parent;
		B::l = o.l;
		B::r = o.r;
		if(B::l) B::l->parent = (Derived*)this;
		if(B::r) B::r->parent = (Derived*)this;
		if(B::parent->l == &o) B::parent->l = (Derived*)this;
		else {A(B::parent->r==&o); B::parent->r = (Derived*)this;}
	}
	inline CopyableSplayNode(const CopyableSplayNode& o) :
		B(o.keyval,o.parent,o.l,o.r)
	{
		if(B::l) B::l->parent = (Derived*)this;
		if(B::r) B::r->parent = (Derived*)this;
		if(B::parent->l == &o) B::parent->l = (Derived*)this;
		else {A(B::parent->r==&o); B::parent->r = (Derived*)this;}
	}
	inline CopyableSplayNode(const _Value& _keyval, Derived* _parent) :
		B(_keyval,_parent) {}
};

// Default SplayNode: copyable, empty update functions
//
// CANNOT BE BASE!
template<typename _Value> struct DefSplayNode :
	public CopyableSplayNode<_Value,DefSplayNode<_Value> >	// tell Base that it's our base
															// (avoid vtable)
{
	typedef CopyableSplayNode<_Value,DefSplayNode<_Value> > B;//ASE

	// Children-less initialization
	inline DefSplayNode(const _Value& _keyval, DefSplayNode* _parent) :
		CopyableSplayNode<_Value,DefSplayNode<_Value> >(_keyval,_parent) {}

	// empty update functions
	inline void update() {}
	inline void updateLR() {A(B::l && B::r);}
	inline void updateL() {A(B::l);}
	inline void updateR() {A(B::r);}
	inline void updateNL() {A(!B::l);}
	inline void updateNR() {A(!B::r);}
	inline void updateCopy(DefSplayNode* x) {}	// copy stats from x
};
////////////////////////////////////////////////////////////////////////////////



}

namespace ab{


///////////////////////////// SPLAY TREE ///////////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2013-2014
//
/*
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
//
// Common SplayTree
//
// new + delete								2.88s
// nodes on vector:							2.81s
// nodes on vector + reserve:				2.76s
// nodes on vector, no copy constructors	2.76s
// after levels optim						2.74s (2.66??)
// splays everywhere, some optimizations	3.08s
// suddenly (after evert?)					3.40s
//
// does not support evert (swapFlag) (TODO?)
template<typename _Key, typename _Value,
	typename _KeyOfVal,
	typename SplayNode = DefSplayNode<_Value>,
	int MaxNodes = 0,
	typename _Alloc = std::allocator<_Value> >
class SplayTree
{
public:
	class iterator;
private:
	typedef _Key key_type;
	typedef _Value value_type;
	typedef _Alloc allocator_type;
	typedef typename _Alloc::template rebind<SplayNode>::other NodeAlloc;
	typedef Splayer<false> SP;	// not evertable!
public:
	inline SplayTree()
	{
		superRoot()->r = NULL;
		superRoot()->l = NULL;
		superRoot()->parent = NULL;
	}
	inline ~SplayTree()
	{
		//A(!superRoot()->r);
		//if(superRoot()->l) _destroyNode(superRoot()->l);
	}
private:
/*
	void _destroyNode(SplayNode *pn)
	{
		if(pn->l) _destroyNode(pn->l);
		if(pn->r) _destroyNode(pn->r);
		nodeAlloc.destroy(pn);
		nodeAlloc.deallocate(pn,1);
	}*/
private:
	SplayNode* newNode(const _Value& _keyval, SplayNode* parent)
	{
		//_v.push_back(node);
		//return &_v.back();
		return new SplayNode(_keyval, parent);
	}
	void delNode(SplayNode* sn)
	{
		//if(sn!=&_v.back()) *sn = _v.back();
		//_v.pop_back();
		delete sn;								// TODO: zwalniac pamiec moze? (!)
	}
public:
	inline iterator find(const value_type& _keyval, const bool splay = true)
	{
		tuple<SplayNode*,SplayNode**,int> re = _find(_keyval);
		SplayNode* pNode = get<0>(re);
		SplayNode** ppNode = get<1>(re);
		int level = get<2>(re);
		if(*ppNode)
		{
			if(splay)
			{
				SP::splayUntilNode(*ppNode,superRoot(),level);
				return iterator(superRoot()->l);
			}
			else return iterator(*ppNode);
		}
		else
		{
			if(splay && level>0) SP::splayUntilNode(pNode,superRoot(),level-1);
			return iterator(superRoot());
		}
	}
	inline pair<iterator,bool> insert(const value_type& _keyval, const bool splay = true)
	{
		//if(_v.size()==_v.capacity())_v.reserve(_v.size()*3/2);
		tuple<SplayNode*,SplayNode**,int> re = _find(_KeyOfVal()(_keyval));
		SplayNode* pNode = get<0>(re);
		SplayNode** ppNode = get<1>(re);
		int level = get<2>(re);
		if(*ppNode)
		{
			auto result = *ppNode;
			if(splay) SP::splayUntilNode(*ppNode,superRoot(),level);
			return make_pair(iterator(result),false);
		}
		else
		{
			//SplayNode nn(_keyval,pNode);
			*ppNode = newNode(_keyval,pNode);
			auto result = *ppNode;
			A(result);
			if(splay){
				SP::splayUntilNode(*ppNode,superRoot(),level);
				result->template update<0,0>();	// TODO: may be unnecessary when there are any splays
			}
			// TODO: update when not splaying
			A(result);
			return make_pair(iterator(result),true);
		}
	}
	inline iterator insertMulti(const value_type& _keyval, const bool splay = true)
	{
		//if(_v.size()==_v.capacity())_v.reserve(_v.size()*3/2);
		pair<SplayNode*,SplayNode**> re = _findForInsert(_KeyOfVal(_keyval));
		re.se = newNode(_keyval,re.fi);
		if(splay) splayToRoot(*re.se,re.th);
		return iterator(re.se);
	}

	inline void erase(const key_type& _key, const bool splay = true)
	{
		erase(find(_key,splay));
	}

	inline void safe_erase(const key_type& _key, const bool splay = true)
	{
		iterator itr = find(_key, splay);
		if(itr != end()) erase(itr);
	}

	inline void erase(const iterator& itr, const bool splay = true)
	{
		A(itr != end());
		_erase(itr.p, splay);
	}

	inline iterator begin()
	{
		SplayNode *pc = superRoot();
		while(pc->l) pc = pc->l;
		return iterator(pc);
	}
	inline iterator end()
	{
		return iterator(superRoot());
	}
	inline bool isRoot(SplayNode* x) const
	{
		return x->parent == NULL;
	}
	inline void clear()
	{
		//_v.clear();
		superRoot()->l = NULL;
	}
	inline void reserve(unsigned int size)
	{
		//_v.reserve(size);
	}

private:
	// assumes x has no children
	inline void _justErase(SplayNode* x)
	{
		A(x != superRoot());
		A(!x->l); A(!x->r);
		if(x->parent->r == x)
		{
			x->parent->r = NULL;
			if(x->parent != superRoot())
			{
				x->parent->template update<0,-1>();//NR
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		else
		{
			A(x->parent->l == x);
			x->parent->l = NULL;
			if(x->parent != superRoot())
			{
				x->parent->template update<-1,0>();//NL
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		delNode(x);
	}
	// assumes x has only left child
	inline void _eraseL(SplayNode* x)
	{
		A(x != superRoot());
		A(x->l); A(!x->r);
		if(x->parent->l == x)
		{
			x->parent->l = x->l;
			if(x->parent != superRoot())
			{
				x->parent->template update<1,0>();//L
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		else
		{
			A(x->parent->r == x);
			x->parent->r = x->l;
			if(x->parent != superRoot())
			{
				x->parent->template update<0,1>();//R
				SP::updateUntilNode(x->parent->parent, superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		x->l->parent = x->parent;
		delNode(x);
	}
	// assumes x has only right child
	inline void _eraseR(SplayNode* x)
	{
		A(x != superRoot());
		A(!x->l); A(x->r);
		if(x->parent->l == x)
		{
			x->parent->l = x->r;
			if(x->parent != superRoot())
			{
				x->parent->template update<1,0>();//L
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		else
		{
			A(x->parent->r == x);
			x->parent->r = x->r;
			if(x->parent != superRoot())
			{
				x->parent->template update<0,1>();//R
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		x->r->parent = x->parent;
		delNode(x);
	}
	// assumes x has both children
	// replaces x with its predecessor
	inline void _eraseIn(SplayNode* const x, const bool splay = true)
	{
		A(x != superRoot());
		A(x->l); A(x->r);
		SplayNode *c = x->l;
		if(c->r)
		{
			c = c->r;
			if(splay)
			{
				int level = 0;
				while(c->r) c = c->r, ++level;
				SplayNode* p = c->parent;
				p->r = c->l;
				if(c->l)
				{
					//c->subVal(c->l);
					c->l->parent = p;
					p->template update<0,1>();//R
				}
				else p->template update<0,-1>();//NR

				int level2 = level/2;
				while(level2)
				{
					SP::rotateL(p->parent);
					SP::rotateL(p);
					--level2;
				}
				if(level&1)
				{
					SP::rotateL(p);
				}
				//p->subVal(c);
				//p->template updateL(c);
				A(p->parent == x);	// splay succeeded
			}
			else // if(!splay)		// TODO: fix updates
			{
				while(c->r) c = c->r;
				c->parent->r = c->l;
				if(c->l)
				{
					c->subVal(c->l);
					c->l->parent = c->parent;
					c->parent->template update<0,1>();//R
				}
				else c->parent->template update<0,-1>();//NR

				c->parent->subVal(c);

				SplayNode *cn = c->parent->parent;
				while(cn != x)
				{
					cn->template update<0,1>();//R
					cn->subVal(c);
					cn = cn->parent;
				}
			}
			c->l = x->l;
			c->l->parent = c;
			c->parent = x->parent;
			if(x->parent->l == x) x->parent->l = c;
			else {A(x->parent->r == x); x->parent->r = c;}
			c->r = x->r;
			c->r->parent = c;
			c->template update<1,1>();//LR
			//c->addVal(c->l);
			//c->addVal(c->r);
		}
		else
		{
			c->parent = x->parent;
			if(x->parent->l == x) x->parent->l = c;
			else {A(x->parent->r == x); x->parent->r = c;}
			c->r = x->r;
			c->r->parent = c;
			c->template update<0,1>();//R
			c->addVal(c->r);
		}
		for(;;)	// TODO: replace with updateUntilNode
		{
			c = c->parent;
			if(c==superRoot())break;
			c->template update<0,0>();
			//c->subVal(x);
		}
		delNode(x);
	}
	// select appriopriate erase function to call
	inline void _erase(SplayNode* x, const bool splay = true, int level = -1)
	{
		SplayNode* parent = x->parent;
		if(x->l)
		{
			if(x->r) _eraseIn(x,splay);
			else _eraseL(x);
		}
		else
		{
			if(x->r) _eraseR(x);
			else _justErase(x);
		}
		
		// splay parent
		if(splay && parent!=superRoot())
		{
			if(level != -1) SP::splayUntilNode(parent,superRoot(),level-1);
			else SP::splayUntilNode(parent,superRoot());
		}
	}
public:
	class iterator
	{	friend class SplayTree;
	public: //private:		// ugly hack?!
		inline iterator(SplayNode *_p) : p(_p) {}
	public:
		inline bool operator==(const iterator& o) const {return p==o.p;}
		inline bool operator!=(const iterator& o) const {return !(*this==o);}
		inline value_type& operator*() {return p->keyval;}
		inline const value_type& operator*() const {return p->keyval;}
		inline value_type* operator->() {return &p->keyval;}
		inline const value_type* operator->() const {return &p->keyval;}
		
		inline SplayNode* getnode(){	// todo: is this an ugly hack?
			return p;
		}
		
		inline iterator& operator++()
		{
			A(p);
			if(p->r)
			{
				p = p->r;
				while(p->l) p = p->l;
			}
			else
			{
				while(p->parent->r == p) p = p->parent;
				p = p->parent;
			}
			return *this;
		}
		inline iterator& operator--()
		{
			A(p);
			if(p->l)
			{
				p = p->l;
				while(p->r) p = p->r;
			}
			else
			{
				while(p->parent->l == p){
					p = p->parent;
					A(p->parent);//!=superRoot());
				}
				p = p->parent;
			}
			return *this;
		}
		inline iterator& operator++(int)
		{
			iterator itr(*this);
			++*this;
			return itr;
		}
		inline iterator& operator--(int)
		{
			iterator itr(*this);
			--*this;
			return itr;
		}
	private:
		SplayNode *p;
	};
public:
	SplayNode& root(){
		A(superRoot()->l);
		return *superRoot()->l;
	}
private:
	//typename _vector<SplayNode,MaxNodes>::R _v;		// TODO: zrobic znowu!

	// super root is not initialized since we only use its l,r,parent pointers
	// it's the greatest node of the tree, has only left son
	char _superRoot[sizeof(SplayNode)];
	inline SplayNode* superRoot()
	{
		SplayNode *sr = reinterpret_cast<SplayNode*>(_superRoot);
		return sr;
	}

	// finds an element and returns <node,parent's pointer to this node, depth(level)>
	inline tuple<SplayNode*,SplayNode**,int> _find(const key_type& _key)
	{
		int level = 0;
		if(superRoot()->l == 0) return make_tuple(superRoot(),&superRoot()->l,0);
		SplayNode *cand = superRoot()->l;
		for(;;) //while(_KeyOfVal()((cand)->keyval) != _key)
		{
			if(_KeyOfVal()((cand)->keyval) < _key)
			{
				++level;
				if((cand)->r) cand = (cand)->r;
				else return make_tuple((cand),&(cand)->r,level);
			}
			else if(_key < _KeyOfVal()((cand)->keyval))
			{
				++level;
				if((cand)->l) cand = (cand)->l;
				else return make_tuple((cand),&(cand)->l,level);
			}
			else break;
		}
		return make_tuple((cand)->parent,
			cand->parent->r==cand?&cand->parent->r:&cand->parent->l,level);
	}
	// finds a place to insert a new element, possibly equal to some others already present
	// returns parent's pointer to this node
	inline SplayNode** _findForInsert(const key_type& _key)	// multiset
	{
		SplayNode **cand = &superRoot()->l;
		while(*cand != NULL)
		{
			if(_KeyOfVal()((*cand)->keyval) <= _key) cand = &(*cand)->r;
			else cand = &(*cand)->l;
		}
		return cand;
	}
};
////////////////////////////////////////////////////// (splay tree) ////////////


template<typename T, class Node = DefSplayNode<T> >
class SplaySet : public SplayTree<T,T,_Identity<T>, Node>{};


}

typedef pair<ll,ll> pll;

struct point{
	ll x,y;
};


int n,m;
int w,h;

struct elem{
	bool operator<(const elem&o)const{
		return pos.y < o.pos.y;
	}
	elem() : pos(point{LLONG_MAX,LLONG_MAX}), val(0) {}
	elem(point p, int v) : pos(p), val(v) {}
	point pos;
	int val;
};

vector<elem> elems;

point tr(int x, int y){
	return point{(ll)x*h - (ll)y*w, (ll)x*h + (ll)y*w};
}


struct node : public CopyableSplayNode<elem,node>
{
	typedef CopyableSplayNode<elem,node> B;//ASE
	
	// Children-less initialization
	node(const elem& _keyval, node* _parent) :
		CopyableSplayNode<elem,node>(_keyval,_parent), sum(0), sufmax(-LLONG_MAX) {}
		
	// splay aggregates
	ll sum;
	ll sufmax;
	
	node* getsufmax(){
		if(r && r->sufmax == sufmax) return r->getsufmax();
		if(!r && sufmax == keyval.val) return this;
		if(r && sufmax == r->sum + keyval.val) return this;
		A(l);
		if(r && sufmax == r->sum + keyval.val + l->sufmax)return l->getsufmax();
		A(!r);
		A(sufmax == keyval.val + l->sufmax);
		return l->getsufmax();
	}
	
	bool getSwapFlag()const {return false;}
	void setSwapFlag(bool) {}
	
	template<int L, int R> void update(){
		sum=keyval.val;
		sufmax = -LLONG_MAX;
		if(L==1 || (L==0 && l)){
			sum += l->sum;
			if(R==1 || r) sufmax = max(sufmax,l->sufmax + keyval.val + r->sum);
			else sufmax = max(sufmax,l->sufmax + keyval.val);
		}
		if(R==1 || (R==0 && r)){
			sum += r->sum;
			sufmax = max(sufmax,r->sufmax);
			sufmax = max(sufmax,keyval.val + r->sum);
		}
		else sufmax = max(sufmax, (ll)keyval.val);
	}
};

// todo: to powinna byŠ mapa
typedef SplaySet<elem,node> SET;
SET secik;


inline void tc()
{
	E<<"welcome."<<N;
	I>>n>>m;
	I>>w>>h;
	
	fo(i,n){
		int x,y,z;
		I>>x>>y>>z;
		elems.pub(elem{tr(x,y),z});
	}
	fo(i,m){
		int x,y,z;
		I>>x>>y>>z;
		elems.pub(elem{tr(x,y),-z});
	}
	
	E<<"sort"<<N;
	sort(all(elems),[](const elem&a,const elem&b){return pll(a.pos.x,-a.pos.y) < pll(b.pos.x,-b.pos.y);});
	
	ll result = 0;
	
	fo(i,elems.sz){
		E<<N<<"PROCESS "<<elems[i].val<<N;
		auto&e = elems[i];
		auto r = secik.insert(e);
		A(&*r.fi);
		if(!r.se){
			r.fi->val += e.val;
			r.fi.getnode()->update<0,0>();
		}
		auto c = r.fi;
		
		E<<"inserted "<<c->val<<N;
		
		// merge right
		E<<"begin merging"<<N;
		for(;;){
			if(c->val <= 0) break;
			auto next = c;
			++next;
			if(next==secik.end()){
				E<<"merge right reached end"<<N;
				A(c->val > 0);
				E<<"merge me hard, honey, be my -LLONG_MAX"<<N;
				//secik.find(*c);	// splay
				c->pos.y = -LLONG_MAX;
				//c.getnode()->update<0,0>();
				break;
			}
			secik.find(*next);	// splay
			E<<next->val<<" += "<<c->val<<N;
			next->val += c->val;
			next.getnode()->update<0,0>();
			secik.erase(c);
			c = next;
		}
		E<<"sufmax is now "<<secik.root().sufmax<<N;
		if(secik.root().sufmax > 0){
			E<<"result += "<<secik.root().sufmax<<N;
			result += secik.root().sufmax;
			auto ee = secik.root().getsufmax();
			A(ee->keyval.val >= 0);
			SET::iterator it(ee);
			int dbgnum = 0;
			for(;;){
				auto last = secik.end();
				--last;
				if(last == it)break;
				secik.erase(last);
				++dbgnum;
			}
			secik.erase(it);
			++dbgnum;
			E<<"  erased "<<dbgnum<<" elements"<<N;
		}
	}
	O<<result<<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

#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 puf push_front
#define pob pop_back()
#define pof pop_front()
#define bs binary_search
#define lb lower_bound
#define ub upper_bound

#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))



#ifdef OLD_COMPILER
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
#include<string>
#include<stdint.h>
#include<cstring>
#include<iostream>
#else
#include<bits/stdc++.h>
#endif





#ifdef OLD_COMPILER

#else
#include<cstdint>
#endif

#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."
#undef FASTIO

#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>



#ifdef OLD_COMPILER
// TODO
#else
#include<type_traits>
#endif


#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(__typeof((c).begin())e=(c).begin();e!=(c).end();++e)


#define MIN_GCC(a,b,c) (__GNUC__ > (a) || \
              (__GNUC__ == (a) && (__GNUC_MINOR__ > (b) || \
                                 (__GNUC_MINOR__ == (b) && \
                                  __GNUC_PATCHLEVEL__ >= (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

#define all(x) (x).be,(x).en
#define type(x) __typeof(x)

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{




#if defined __GNUC__ and not MIN_GCC(4,2,0)
template<class T>struct hash<T>{}
#endif

// 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 uniqall(T&t){t.resize(unique(t.be,t.en)-t.be);}

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













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{


//////////////////////// SPLAYER (for splay trees) /////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2013-2014
//
/*
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
//
// Splayer provides some splay node operations
template<bool evertable = false>
struct Splayer
{
	template<typename PV>
	static inline void updateUntilNode(PV x, const PV& superRoot)
	{
		while(x != superRoot)
		{
			A(x);
			x->template update<0,0>();
			x = x->parent;
		}
	}
	template<typename SplayNode>
	static inline void updateUntilNull(SplayNode* x)
	{
		updateUntilNode(x,NULL);
	}
	template<typename SplayNode>
	static inline void splayUntilNode(SplayNode *x,
		const SplayNode* const superRoot, int level)
	{
		//int level = 0;
		//SplayNode *pc = x;
		//while(pc->parent != superRoot()) pc = pc->parent, ++level;
		int level2 = level/2;
		while(level2) splay(x),--level2;
		if(level&1) rotate(x);
		A(x->parent == superRoot);
	}
	template<typename SplayNode>
	static inline void splayUntilNode(SplayNode *x, SplayNode *superRoot)
	{
		int level = 0;
		SplayNode *pc = x;
		while(pc->parent != superRoot) pc = pc->parent, ++level;
		splayUntilNode(x,superRoot,level);
	}
	template<typename SplayNode>
	static inline void splayUntilNull(SplayNode *x, int level)
	{
		if(level==0)return;
		if(level==1)rotateLast(x);
		else
		{
			int level2 = level/2;
			while(--level2) splay(x);
			if(level&1) splay(x),rotateLast(x);
			else splayLast(x);
		}
		A(x->parent == NULL);
	}
	// returns previous root
	template<typename SplayNode>
	static inline SplayNode* splayUntilNull(SplayNode *x)
	{
		int level = 0;
		SplayNode *pc = x;
		while(pc->parent) pc = pc->parent, ++level;
		splayUntilNull(x,level);
		return pc;
	}

	// splay only right
	template<typename SplayNode>
	static inline void splayRUntilNull(SplayNode *x, int level)
	{
		if(level==0)return;
		if(level==1)rotateRLast(x);
		else
		{
			int level2 = level/2;
			while(--level2) rotateR(x->parent),rotateR(x);
			if(level&1) rotateR(x->parent),rotateR(x),rotateRLast(x);
			else rotateRLast(x->parent),rotateRLast(x);
		}
		A(x->parent == NULL);
	}
	// returns previous root
	template<typename SplayNode>
	static inline SplayNode* splayRUntilNull(SplayNode *x)
	{
		int level = 0;
		SplayNode *pc = x;
		while(pc->parent) pc = pc->parent, ++level;
		splayRUntilNull(x,level);	// bugfix
		return pc;
	}


	// ROTATIONS

	// assumes x's parent is NOT root (its parent != NULL)
	template<typename SplayNode>
	static inline void rotateR(SplayNode* x)
	{
		A(x->parent && x->parent->parent);
		SplayNode *prevParent = rotateRLast(x);
		A(x->parent);
		if(x->parent->l == prevParent) x->parent->l = x;
		else {A(x->parent->r == prevParent); x->parent->r = x;}
	}
	// assumes x's parent is root (its parent == NULL)
	// return prev parent
	template<typename SplayNode>
	static inline SplayNode* rotateRLast(SplayNode* x)
	{
		A(x); A(x->parent);
		A(x->parent->l == x);	// can rotate right
		SplayNode *parent = x->parent;
		SplayNode* xr;
		if(evertable && x->getSwapFlag())
		{
			xr = x->l;
			x->l = x->r;
			if(x->l) x->l->setSwapFlag(!x->l->getSwapFlag());
			if(xr) xr->setSwapFlag(!xr->getSwapFlag());
		}
		else
		{
			xr = x->r;
		}
		parent->l = xr;
		//parent->subVal(x);
		//parent->addVal(xr);
		//x->subVal(xr);
		//x->addVal(parent);
		
		//x->updateCopy(parent);
		if(xr)
		{
			xr->parent = parent;
			parent->template update<1,0>();	// L
		}
		else parent->template update<-1,0>();	// NL
		x->parent = parent->parent;
		x->setSwapFlag(parent->getSwapFlag());
		parent->setSwapFlag(false);
		x->r = parent;
		parent->parent = x;
		x->template update<0,1>();
		return parent;
	}
	// assumes x's parent is NOT root (its parent != NULL)
	template<typename SplayNode>
	static inline void rotateL(SplayNode* x)
	{
		A(x->parent->parent);
		SplayNode *prevParent = rotateLLast(x);
		if(x->parent->l == prevParent) x->parent->l = x;
		else {A(x->parent->r == prevParent); x->parent->r = x;}
	}
	// assumes x's parent is root (its parent == NULL)
	// returns prev parent
	template<typename SplayNode>
	static inline SplayNode* rotateLLast(SplayNode* x)
	{
		A(x); A(x->parent);
		A(x->parent->r == x);	// can rotate left
		SplayNode *parent = x->parent;
		SplayNode *xl;
		if(evertable && x->getSwapFlag())
		{
			xl = x->r;
			x->r = x->l;
			if(x->r) x->r->setSwapFlag(!x->r->getSwapFlag());
			if(xl) xl->setSwapFlag(!xl->getSwapFlag());
		}
		else
		{
			xl = x->l;
		}
		parent->r = xl;
		//parent->subVal(x);
		//parent->addVal(xl);
		//x->subVal(xl);
		//x->addVal(parent);
		//x->updateCopy(parent);
		if(xl)
		{
			xl->parent = x->parent;
			parent->template update<0,1>();	// R
		}
		else parent->template update<0,-1>(); // NR
		x->parent = parent->parent;
		x->setSwapFlag(parent->getSwapFlag());
		parent->setSwapFlag(false);
		x->l = parent;
		parent->parent = x;
		x->template update<1,0>();
		return parent;
	}
	// assumes x's parent is NOT root (its parent != null)
	template<typename SplayNode>
	static inline void rotate(SplayNode* x)
	{
		A(x); A(x->parent); A(x->parent->parent);
		if(x->parent->r == x) rotateL(x);
		else {A(x->parent->l == x); rotateR(x);}
	}
	// assumes x's parent is root (its parent == null)
	template<typename SplayNode>
	static inline void rotateLast(SplayNode* x)
	{
		A(x); A(x->parent);A(!x->parent->parent);
		if(x->parent->r == x) rotateLLast(x);
		else {A(x->parent->l == x); rotateRLast(x);}
	}

	// assumes x's grandparent is NOT root (its parent != NULL)
	template<typename SplayNode>	// TODO: can be optimized if splays aren't
									// done using rotate functions but directly
	static inline void splay(SplayNode *x)	// zig-zig or zig-zag
	{
		A(x); A(x->parent); // x not root
		A(x->parent->parent); // parent not root
		A(x->parent->parent->parent); // there is superRoot
		SplayNode *p = x->parent;
		SplayNode *g = p->parent;
		if(evertable && p->getSwapFlag())
		{
			if(p->l == x)
			{
				if(g->l == p) rotateR(x), rotateR(x);
				else {A(g->r == p); rotateL(p), rotateL(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateR(p), rotateR(x);
				else {A(g->r == p); rotateL(x), rotateL(x);}
			}
		}
		else
		{
			if(p->l == x)
			{
				if(g->l == p) rotateR(p), rotateR(x);
				else {A(g->r == p); rotateR(x), rotateL(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateL(x), rotateR(x);
				else {A(g->r == p); rotateL(p), rotateL(x);}
			}
		}
	}

	// assumes x's grandparent is root (its parent == NULL)
	template<typename SplayNode>
	static inline void splayLast(SplayNode *x)	// zig-zig or zig-zag
	{
		A(x); A(x->parent); // x not root
		A(x->parent->parent); // parent not root
		SplayNode *p = x->parent;
		SplayNode *g = p->parent;
		if(evertable && p->getSwapFlag())
		{
			if(p->l == x)
			{
				if(g->l == p) rotateR(x), rotateRLast(x);
				else {A(g->r == p); rotateLLast(p), rotateLLast(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateRLast(p), rotateRLast(x);
				else {A(g->r == p); rotateL(x), rotateLLast(x);}
			}
		}
		else
		{
			if(p->l == x)
			{
				if(g->l == p) rotateRLast(p), rotateRLast(x);
				else {A(g->r == p); rotateR(x), rotateLLast(x);}
			}
			else
			{
				A(p->r == x);
				if(g->l == p) rotateL(x), rotateRLast(x);
				else {A(g->r == p); rotateLLast(p), rotateLLast(x);}
			}
		}
	}
	// debug
	template<typename SplayNode>
	static inline bool consistent(const SplayNode *pv)
	{
		// parent link
		if(pv->parent && pv->parent->l!=pv && pv->parent->r!=pv) return false;
		// left link
		if(pv->l && pv->l->parent!=pv) return false;
		// right link
		if(pv->r && pv->r->parent!=pv) return false;
		// children are the same
		if(pv->l && pv->l == pv->r) return false;
		if(pv->l && pv->l == pv->parent) return false;
		if(pv->r && pv->r == pv->parent) return false;
		return true;
	}
};
////////////////////////////////////////////////////////////////////////////////



}


namespace ab{


////////////////////////// SPLAY NODES /////////////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2013-2014
//
/*
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
//
template<typename _Value, typename Derived> struct BaseSplayNode
{
	// Only data, should be no vptr
	_Value keyval;
	Derived *parent;
	Derived *l;
	Derived *r;

	// Children-less initialization
	inline BaseSplayNode(const _Value& _keyval, Derived* _parent) :
		keyval(_keyval), parent(_parent), l(NULL), r(NULL) {}

	// Full initialization
	inline BaseSplayNode(const _Value& _keyval, Derived* _parent, Derived* _l, Derived* __r) :
		keyval(_keyval), parent(_parent), l(_l), r(__r) {}

	// PATH AGGREGATION
	// "pure virtual" update functions
	inline void update() {A(false);}
	inline void updateLR() {A(l && r);A(false);}
	inline void updateL() {A(l);A(false);}
	inline void updateR() {A(r);A(false);}
	inline void updateNL() {A(!l);A(false);}
	inline void updateNR() {A(!r);A(false);}
	inline void updateCopy(Derived* x) {A(false);}	// copy stats from x

	// TODO: path aggregation for linear values - could be faster,
	//   especially when updating ancestors of deleted node

	// swap flag - for evert (rerooting)
	inline bool getSwapFlag() const {A(false); return 0;}
	inline void setSwapFlag(bool) {A(false);}

	// TREE AGGREGATION (only linear values)
	// suitable for sum, not suitable for max
	inline void addVal(Derived* x) {A(false);}
	inline void subVal(Derived* x) {A(false);}
};
template<typename _Value, typename Derived> struct CopyableSplayNode :
	public BaseSplayNode<_Value, Derived>
{
	typedef BaseSplayNode<_Value,Derived> B;//ASE
	inline void operator=(const CopyableSplayNode& o)
	{
		B::keyval = o.keyval;
		B::parent = o.parent;
		B::l = o.l;
		B::r = o.r;
		if(B::l) B::l->parent = (Derived*)this;
		if(B::r) B::r->parent = (Derived*)this;
		if(B::parent->l == &o) B::parent->l = (Derived*)this;
		else {A(B::parent->r==&o); B::parent->r = (Derived*)this;}
	}
	inline CopyableSplayNode(const CopyableSplayNode& o) :
		B(o.keyval,o.parent,o.l,o.r)
	{
		if(B::l) B::l->parent = (Derived*)this;
		if(B::r) B::r->parent = (Derived*)this;
		if(B::parent->l == &o) B::parent->l = (Derived*)this;
		else {A(B::parent->r==&o); B::parent->r = (Derived*)this;}
	}
	inline CopyableSplayNode(const _Value& _keyval, Derived* _parent) :
		B(_keyval,_parent) {}
};

// Default SplayNode: copyable, empty update functions
//
// CANNOT BE BASE!
template<typename _Value> struct DefSplayNode :
	public CopyableSplayNode<_Value,DefSplayNode<_Value> >	// tell Base that it's our base
															// (avoid vtable)
{
	typedef CopyableSplayNode<_Value,DefSplayNode<_Value> > B;//ASE

	// Children-less initialization
	inline DefSplayNode(const _Value& _keyval, DefSplayNode* _parent) :
		CopyableSplayNode<_Value,DefSplayNode<_Value> >(_keyval,_parent) {}

	// empty update functions
	inline void update() {}
	inline void updateLR() {A(B::l && B::r);}
	inline void updateL() {A(B::l);}
	inline void updateR() {A(B::r);}
	inline void updateNL() {A(!B::l);}
	inline void updateNR() {A(!B::r);}
	inline void updateCopy(DefSplayNode* x) {}	// copy stats from x
};
////////////////////////////////////////////////////////////////////////////////



}

namespace ab{


///////////////////////////// SPLAY TREE ///////////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2013-2014
//
/*
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
//
// Common SplayTree
//
// new + delete								2.88s
// nodes on vector:							2.81s
// nodes on vector + reserve:				2.76s
// nodes on vector, no copy constructors	2.76s
// after levels optim						2.74s (2.66??)
// splays everywhere, some optimizations	3.08s
// suddenly (after evert?)					3.40s
//
// does not support evert (swapFlag) (TODO?)
template<typename _Key, typename _Value,
	typename _KeyOfVal,
	typename SplayNode = DefSplayNode<_Value>,
	int MaxNodes = 0,
	typename _Alloc = std::allocator<_Value> >
class SplayTree
{
public:
	class iterator;
private:
	typedef _Key key_type;
	typedef _Value value_type;
	typedef _Alloc allocator_type;
	typedef typename _Alloc::template rebind<SplayNode>::other NodeAlloc;
	typedef Splayer<false> SP;	// not evertable!
public:
	inline SplayTree()
	{
		superRoot()->r = NULL;
		superRoot()->l = NULL;
		superRoot()->parent = NULL;
	}
	inline ~SplayTree()
	{
		//A(!superRoot()->r);
		//if(superRoot()->l) _destroyNode(superRoot()->l);
	}
private:
/*
	void _destroyNode(SplayNode *pn)
	{
		if(pn->l) _destroyNode(pn->l);
		if(pn->r) _destroyNode(pn->r);
		nodeAlloc.destroy(pn);
		nodeAlloc.deallocate(pn,1);
	}*/
private:
	SplayNode* newNode(const _Value& _keyval, SplayNode* parent)
	{
		//_v.push_back(node);
		//return &_v.back();
		return new SplayNode(_keyval, parent);
	}
	void delNode(SplayNode* sn)
	{
		//if(sn!=&_v.back()) *sn = _v.back();
		//_v.pop_back();
		delete sn;								// TODO: zwalniac pamiec moze? (!)
	}
public:
	inline iterator find(const value_type& _keyval, const bool splay = true)
	{
		tuple<SplayNode*,SplayNode**,int> re = _find(_keyval);
		SplayNode* pNode = get<0>(re);
		SplayNode** ppNode = get<1>(re);
		int level = get<2>(re);
		if(*ppNode)
		{
			if(splay)
			{
				SP::splayUntilNode(*ppNode,superRoot(),level);
				return iterator(superRoot()->l);
			}
			else return iterator(*ppNode);
		}
		else
		{
			if(splay && level>0) SP::splayUntilNode(pNode,superRoot(),level-1);
			return iterator(superRoot());
		}
	}
	inline pair<iterator,bool> insert(const value_type& _keyval, const bool splay = true)
	{
		//if(_v.size()==_v.capacity())_v.reserve(_v.size()*3/2);
		tuple<SplayNode*,SplayNode**,int> re = _find(_KeyOfVal()(_keyval));
		SplayNode* pNode = get<0>(re);
		SplayNode** ppNode = get<1>(re);
		int level = get<2>(re);
		if(*ppNode)
		{
			auto result = *ppNode;
			if(splay) SP::splayUntilNode(*ppNode,superRoot(),level);
			return make_pair(iterator(result),false);
		}
		else
		{
			//SplayNode nn(_keyval,pNode);
			*ppNode = newNode(_keyval,pNode);
			auto result = *ppNode;
			A(result);
			if(splay){
				SP::splayUntilNode(*ppNode,superRoot(),level);
				result->template update<0,0>();	// TODO: may be unnecessary when there are any splays
			}
			// TODO: update when not splaying
			A(result);
			return make_pair(iterator(result),true);
		}
	}
	inline iterator insertMulti(const value_type& _keyval, const bool splay = true)
	{
		//if(_v.size()==_v.capacity())_v.reserve(_v.size()*3/2);
		pair<SplayNode*,SplayNode**> re = _findForInsert(_KeyOfVal(_keyval));
		re.se = newNode(_keyval,re.fi);
		if(splay) splayToRoot(*re.se,re.th);
		return iterator(re.se);
	}

	inline void erase(const key_type& _key, const bool splay = true)
	{
		erase(find(_key,splay));
	}

	inline void safe_erase(const key_type& _key, const bool splay = true)
	{
		iterator itr = find(_key, splay);
		if(itr != end()) erase(itr);
	}

	inline void erase(const iterator& itr, const bool splay = true)
	{
		A(itr != end());
		_erase(itr.p, splay);
	}

	inline iterator begin()
	{
		SplayNode *pc = superRoot();
		while(pc->l) pc = pc->l;
		return iterator(pc);
	}
	inline iterator end()
	{
		return iterator(superRoot());
	}
	inline bool isRoot(SplayNode* x) const
	{
		return x->parent == NULL;
	}
	inline void clear()
	{
		//_v.clear();
		superRoot()->l = NULL;
	}
	inline void reserve(unsigned int size)
	{
		//_v.reserve(size);
	}

private:
	// assumes x has no children
	inline void _justErase(SplayNode* x)
	{
		A(x != superRoot());
		A(!x->l); A(!x->r);
		if(x->parent->r == x)
		{
			x->parent->r = NULL;
			if(x->parent != superRoot())
			{
				x->parent->template update<0,-1>();//NR
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		else
		{
			A(x->parent->l == x);
			x->parent->l = NULL;
			if(x->parent != superRoot())
			{
				x->parent->template update<-1,0>();//NL
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		delNode(x);
	}
	// assumes x has only left child
	inline void _eraseL(SplayNode* x)
	{
		A(x != superRoot());
		A(x->l); A(!x->r);
		if(x->parent->l == x)
		{
			x->parent->l = x->l;
			if(x->parent != superRoot())
			{
				x->parent->template update<1,0>();//L
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		else
		{
			A(x->parent->r == x);
			x->parent->r = x->l;
			if(x->parent != superRoot())
			{
				x->parent->template update<0,1>();//R
				SP::updateUntilNode(x->parent->parent, superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		x->l->parent = x->parent;
		delNode(x);
	}
	// assumes x has only right child
	inline void _eraseR(SplayNode* x)
	{
		A(x != superRoot());
		A(!x->l); A(x->r);
		if(x->parent->l == x)
		{
			x->parent->l = x->r;
			if(x->parent != superRoot())
			{
				x->parent->template update<1,0>();//L
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		else
		{
			A(x->parent->r == x);
			x->parent->r = x->r;
			if(x->parent != superRoot())
			{
				x->parent->template update<0,1>();//R
				SP::updateUntilNode(x->parent->parent,superRoot());
				//SP::subUntilNode(x->parent,x,superRoot());
			}
		}
		x->r->parent = x->parent;
		delNode(x);
	}
	// assumes x has both children
	// replaces x with its predecessor
	inline void _eraseIn(SplayNode* const x, const bool splay = true)
	{
		A(x != superRoot());
		A(x->l); A(x->r);
		SplayNode *c = x->l;
		if(c->r)
		{
			c = c->r;
			if(splay)
			{
				int level = 0;
				while(c->r) c = c->r, ++level;
				SplayNode* p = c->parent;
				p->r = c->l;
				if(c->l)
				{
					//c->subVal(c->l);
					c->l->parent = p;
					p->template update<0,1>();//R
				}
				else p->template update<0,-1>();//NR

				int level2 = level/2;
				while(level2)
				{
					SP::rotateL(p->parent);
					SP::rotateL(p);
					--level2;
				}
				if(level&1)
				{
					SP::rotateL(p);
				}
				//p->subVal(c);
				//p->template updateL(c);
				A(p->parent == x);	// splay succeeded
			}
			else // if(!splay)		// TODO: fix updates
			{
				while(c->r) c = c->r;
				c->parent->r = c->l;
				if(c->l)
				{
					c->subVal(c->l);
					c->l->parent = c->parent;
					c->parent->template update<0,1>();//R
				}
				else c->parent->template update<0,-1>();//NR

				c->parent->subVal(c);

				SplayNode *cn = c->parent->parent;
				while(cn != x)
				{
					cn->template update<0,1>();//R
					cn->subVal(c);
					cn = cn->parent;
				}
			}
			c->l = x->l;
			c->l->parent = c;
			c->parent = x->parent;
			if(x->parent->l == x) x->parent->l = c;
			else {A(x->parent->r == x); x->parent->r = c;}
			c->r = x->r;
			c->r->parent = c;
			c->template update<1,1>();//LR
			//c->addVal(c->l);
			//c->addVal(c->r);
		}
		else
		{
			c->parent = x->parent;
			if(x->parent->l == x) x->parent->l = c;
			else {A(x->parent->r == x); x->parent->r = c;}
			c->r = x->r;
			c->r->parent = c;
			c->template update<0,1>();//R
			c->addVal(c->r);
		}
		for(;;)	// TODO: replace with updateUntilNode
		{
			c = c->parent;
			if(c==superRoot())break;
			c->template update<0,0>();
			//c->subVal(x);
		}
		delNode(x);
	}
	// select appriopriate erase function to call
	inline void _erase(SplayNode* x, const bool splay = true, int level = -1)
	{
		SplayNode* parent = x->parent;
		if(x->l)
		{
			if(x->r) _eraseIn(x,splay);
			else _eraseL(x);
		}
		else
		{
			if(x->r) _eraseR(x);
			else _justErase(x);
		}
		
		// splay parent
		if(splay && parent!=superRoot())
		{
			if(level != -1) SP::splayUntilNode(parent,superRoot(),level-1);
			else SP::splayUntilNode(parent,superRoot());
		}
	}
public:
	class iterator
	{	friend class SplayTree;
	public: //private:		// ugly hack?!
		inline iterator(SplayNode *_p) : p(_p) {}
	public:
		inline bool operator==(const iterator& o) const {return p==o.p;}
		inline bool operator!=(const iterator& o) const {return !(*this==o);}
		inline value_type& operator*() {return p->keyval;}
		inline const value_type& operator*() const {return p->keyval;}
		inline value_type* operator->() {return &p->keyval;}
		inline const value_type* operator->() const {return &p->keyval;}
		
		inline SplayNode* getnode(){	// todo: is this an ugly hack?
			return p;
		}
		
		inline iterator& operator++()
		{
			A(p);
			if(p->r)
			{
				p = p->r;
				while(p->l) p = p->l;
			}
			else
			{
				while(p->parent->r == p) p = p->parent;
				p = p->parent;
			}
			return *this;
		}
		inline iterator& operator--()
		{
			A(p);
			if(p->l)
			{
				p = p->l;
				while(p->r) p = p->r;
			}
			else
			{
				while(p->parent->l == p){
					p = p->parent;
					A(p->parent);//!=superRoot());
				}
				p = p->parent;
			}
			return *this;
		}
		inline iterator& operator++(int)
		{
			iterator itr(*this);
			++*this;
			return itr;
		}
		inline iterator& operator--(int)
		{
			iterator itr(*this);
			--*this;
			return itr;
		}
	private:
		SplayNode *p;
	};
public:
	SplayNode& root(){
		A(superRoot()->l);
		return *superRoot()->l;
	}
private:
	//typename _vector<SplayNode,MaxNodes>::R _v;		// TODO: zrobic znowu!

	// super root is not initialized since we only use its l,r,parent pointers
	// it's the greatest node of the tree, has only left son
	char _superRoot[sizeof(SplayNode)];
	inline SplayNode* superRoot()
	{
		SplayNode *sr = reinterpret_cast<SplayNode*>(_superRoot);
		return sr;
	}

	// finds an element and returns <node,parent's pointer to this node, depth(level)>
	inline tuple<SplayNode*,SplayNode**,int> _find(const key_type& _key)
	{
		int level = 0;
		if(superRoot()->l == 0) return make_tuple(superRoot(),&superRoot()->l,0);
		SplayNode *cand = superRoot()->l;
		for(;;) //while(_KeyOfVal()((cand)->keyval) != _key)
		{
			if(_KeyOfVal()((cand)->keyval) < _key)
			{
				++level;
				if((cand)->r) cand = (cand)->r;
				else return make_tuple((cand),&(cand)->r,level);
			}
			else if(_key < _KeyOfVal()((cand)->keyval))
			{
				++level;
				if((cand)->l) cand = (cand)->l;
				else return make_tuple((cand),&(cand)->l,level);
			}
			else break;
		}
		return make_tuple((cand)->parent,
			cand->parent->r==cand?&cand->parent->r:&cand->parent->l,level);
	}
	// finds a place to insert a new element, possibly equal to some others already present
	// returns parent's pointer to this node
	inline SplayNode** _findForInsert(const key_type& _key)	// multiset
	{
		SplayNode **cand = &superRoot()->l;
		while(*cand != NULL)
		{
			if(_KeyOfVal()((*cand)->keyval) <= _key) cand = &(*cand)->r;
			else cand = &(*cand)->l;
		}
		return cand;
	}
};
////////////////////////////////////////////////////// (splay tree) ////////////


template<typename T, class Node = DefSplayNode<T> >
class SplaySet : public SplayTree<T,T,_Identity<T>, Node>{};


}

typedef pair<ll,ll> pll;

struct point{
	ll x,y;
};


int n,m;
int w,h;

struct elem{
	bool operator<(const elem&o)const{
		return pos.y < o.pos.y;
	}
	elem() : pos(point{LLONG_MAX,LLONG_MAX}), val(0) {}
	elem(point p, int v) : pos(p), val(v) {}
	point pos;
	int val;
};

vector<elem> elems;

point tr(int x, int y){
	return point{(ll)x*h - (ll)y*w, (ll)x*h + (ll)y*w};
}


struct node : public CopyableSplayNode<elem,node>
{
	typedef CopyableSplayNode<elem,node> B;//ASE
	
	// Children-less initialization
	node(const elem& _keyval, node* _parent) :
		CopyableSplayNode<elem,node>(_keyval,_parent), sum(0), sufmax(-LLONG_MAX) {}
		
	// splay aggregates
	ll sum;
	ll sufmax;
	
	node* getsufmax(){
		if(r && r->sufmax == sufmax) return r->getsufmax();
		if(!r && sufmax == keyval.val) return this;
		if(r && sufmax == r->sum + keyval.val) return this;
		A(l);
		if(r && sufmax == r->sum + keyval.val + l->sufmax)return l->getsufmax();
		A(!r);
		A(sufmax == keyval.val + l->sufmax);
		return l->getsufmax();
	}
	
	bool getSwapFlag()const {return false;}
	void setSwapFlag(bool) {}
	
	template<int L, int R> void update(){
		sum=keyval.val;
		sufmax = -LLONG_MAX;
		if(L==1 || (L==0 && l)){
			sum += l->sum;
			if(R==1 || r) sufmax = max(sufmax,l->sufmax + keyval.val + r->sum);
			else sufmax = max(sufmax,l->sufmax + keyval.val);
		}
		if(R==1 || (R==0 && r)){
			sum += r->sum;
			sufmax = max(sufmax,r->sufmax);
			sufmax = max(sufmax,keyval.val + r->sum);
		}
		else sufmax = max(sufmax, (ll)keyval.val);
	}
};

// todo: to powinna byŠ mapa
typedef SplaySet<elem,node> SET;
SET secik;


inline void tc()
{
	E<<"welcome."<<N;
	I>>n>>m;
	I>>w>>h;
	
	fo(i,n){
		int x,y,z;
		I>>x>>y>>z;
		elems.pub(elem{tr(x,y),z});
	}
	fo(i,m){
		int x,y,z;
		I>>x>>y>>z;
		elems.pub(elem{tr(x,y),-z});
	}
	
	E<<"sort"<<N;
	sort(all(elems),[](const elem&a,const elem&b){return pll(a.pos.x,-a.pos.y) < pll(b.pos.x,-b.pos.y);});
	
	ll result = 0;
	
	fo(i,elems.sz){
		E<<N<<"PROCESS "<<elems[i].val<<N;
		auto&e = elems[i];
		auto r = secik.insert(e);
		A(&*r.fi);
		if(!r.se){
			r.fi->val += e.val;
			r.fi.getnode()->update<0,0>();
		}
		auto c = r.fi;
		
		E<<"inserted "<<c->val<<N;
		
		// merge right
		E<<"begin merging"<<N;
		for(;;){
			if(c->val <= 0) break;
			auto next = c;
			++next;
			if(next==secik.end()){
				E<<"merge right reached end"<<N;
				A(c->val > 0);
				E<<"merge me hard, honey, be my -LLONG_MAX"<<N;
				//secik.find(*c);	// splay
				c->pos.y = -LLONG_MAX;
				//c.getnode()->update<0,0>();
				break;
			}
			secik.find(*next);	// splay
			E<<next->val<<" += "<<c->val<<N;
			next->val += c->val;
			next.getnode()->update<0,0>();
			secik.erase(c);
			c = next;
		}
		E<<"sufmax is now "<<secik.root().sufmax<<N;
		if(secik.root().sufmax > 0){
			E<<"result += "<<secik.root().sufmax<<N;
			result += secik.root().sufmax;
			auto ee = secik.root().getsufmax();
			A(ee->keyval.val >= 0);
			SET::iterator it(ee);
			int dbgnum = 0;
			for(;;){
				auto last = secik.end();
				--last;
				if(last == it)break;
				secik.erase(last);
				++dbgnum;
			}
			secik.erase(it);
			++dbgnum;
			E<<"  erased "<<dbgnum<<" elements"<<N;
		}
	}
	O<<result<<N;
}