// RBTree
#define BLACK 0
#define RED 1
typedef int Int
Struct RBNode{
RBNode *chi[2],*pa;
int color,cnt;
}*nil=new RBNode(),*root=nil;
void Nil(){ CreatNode(nil,0,BLACK,0); }
RBNode * CreatNode(RBNode * &node,Int val,int color,int cnt=1){
if(node!=NULL && node!=nil){ RBNode *p=node; delete p; }
node=new RBNode(); node->val=val; node->cnt=cnt;
node->pa=node->chi[0]=node->chi[1]=nil; return node;
}
void Connect(RBNode *pa,RBNode *node,int dir)
{ Nil(); pa->chi[dir]=node; node->pa=pa; Nil(); }
RBNode * Extrema(RBNode * node,int dir){
while(node->chi[dir]!=nil) node=node->chi[dir];
return node;
}
RBNode * Cessor(RBNode * node,int dir){
if(node->chi[dir]!=nil) return Extrema(node->chi[dir],1-dir);
for(RBNode * p=node->pa;p!=nil && p->chi[dir]==node;node=p,p=p->pa);
return node->pa;
}
RBNode * Bound(RBNode * node,Int val,int dif=1){
if(node==nil) return nil;
for(int dir;val!=node->val;node=node->chi[dir]){
dir=(val<node->val)?0:1;
if(node->chi[dir]==nil) return node;
}
if(!dif && node->val!=val) return nil;
return node;
}
void Rotate(RBNode *node,int rodir){
Nil(); RBNode *pivot=node->chi[1-rodir];
Connect(node,node->chi[1-rodir]->chi[rodir],1-rodir);
Connect(node->pa,pivot,(node->pa->chi[0]==node)?0:1);
Connect(pivot,node,rodir); Nil();
if(root==node) root=pivot;
}
void Fixup(RBNode *root,RBNode *node){
}
void Insert(RBNode * &root,Int val){
if(root==nil){ root=CreatNode(root,val,RED); return; }
Nil(); RBNode *p=Bound(root,val,1);
if(p->val==val){ p->cnt++; return; }
int dir=(val<p->val)?0:1; RBNode *node=nil;
CreatNode(node,val); Connect(p,node,dir);
Fixup(root,node); Nil();
}
bool Delete(RBNode *&root,Int val){
if(root==nil) return false;
Nil(); if((RBNode *p=Bound(root,val,0))==nil) return false;
if(p->cnt>1){ (p->cnt)--; return true; }
if(p->chi[0]!=nil || p->chi[1]!=nil)
if((RBNode *suc=Cessor(p,1))!=nil || (suc=Cessor(p,0))!=nil)
{p->val=suc->val; p->cnt=suc->cnt; p=suc; }
int dir=p->pa->chi[0]==p?0:1; p->pa->chi[dir]=nil; p=p->pa;
Balance(p,(!dir)?1:-1,1);
if(p!=root) delete p; else {RBNode * t=p; root=nil; delete t;}
Nil(); return true;
}
//-------------
void Insert(BFNode * node,Int val){
BFNode *x=root;
while(node->chi!=nil){
x=x->chi;
if(x->size=4) Split(x);
}
if(x->size==2) x.Plus(val);
else if(x->size==3) x.Plus4(val);
return x;
}
//----------------
RBNode * Insert(RBNode node,Int key,Int val){
if(node==nil) return node=CreatNode(node,key,val);
int cmp=Cmp(key,node->key);
if(cmp==0) node->val=val;
else if(cmp<0) Insert(node->chi[0],key,val);
else Insert(node->chi[1],key,val);
return Node;
}
void ColorFlip(RBNode * node)
{ node->color^=1; node->chi[0].color^=1; node->chi[1].color^=1; }
//---------
RBNode * Insert(RBNode * node,Int key,Int val){
if(node==nil) return node=CreatNode(node,key,val,RED);
int cmp=Cmp(key,node->key);
if(cmp==0) node->val=val;
else if(cmp<0) Insert(node->chi[0],key,val);
else Insert(node->chi[1],key,val);
if(node->chi[1].color==RED) Rotate(node,0);
if(node->chi[0].color==RED && node->chi[1].color==RED) Rotate(node,1);
if(node->chi[0]->color==RED && node->chi[1].color==RED) ColorFlip(node);
return Node;
}
RBNode * Delete(RBNode * node,Int key){
if(key<node->key){
if(node->chi[0]->color==RED && node->chi[0]->chi[0]->color==RED){
MoveRedLeft(node); node->chi[0]=Delete(node->chi[0],key);
}else{
if(node->chi[0]->color==RED) node=LeanRight(node);
if(key==node->key && node->chi[1]==nil) return nil;
if(node->chi[1]->color!=RED && node->chi[1]->chi[0]->color!=RED) node=MoveREDRight(node);
if(node->key==key)
{ node->key=min(node->chi[1]); node->val=Get(node->chi[1],node->key); node->chi[1]=DeleteMin(node->chi[1]); }
else node->chi[1]=Delete(node->chi[1],key);
}
}
return Fixup(node);
]
