import sys readline=sys.stdin.readline from collections import deque # https://github.com/tatyam-prime/SortedSet/blob/main/SortedSet.py import math from bisect import bisect_left, bisect_right, insort from typing import Generic, Iterable, Iterator, TypeVar, Optional, List T = TypeVar('T') class SortedSet(Generic[T]): BUCKET_RATIO = 50 REBUILD_RATIO = 170 def _build(self, a: Optional[List[T]] = None) -> None: "Evenly divide `a` into buckets." if a is None: a = list(self) size = self.size = len(a) bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO))) self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)] def __init__(self, a: Iterable[T] = []) -> None: "Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)" a = list(a) if not all(a[i] < a[i + 1] for i in range(len(a) - 1)): a = sorted(set(a)) self._build(a) def __iter__(self) -> Iterator[T]: for i in self.a: for j in i: yield j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __eq__(self, other) -> bool: return list(self) == list(other) def __len__(self) -> int: return self.size def __repr__(self) -> str: return "SortedSet" + str(self.a) def __str__(self) -> str: s = str(list(self)) return "{" + s[1 : len(s) - 1] + "}" def _find_bucket(self, x: T) -> List[T]: "Find the bucket which should contain x. self must not be empty." for a in self.a: if x <= a[-1]: return a return a def __contains__(self, x: T) -> bool: if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) return i != len(a) and a[i] == x def add(self, x: T) -> bool: "Add an element and return True if added. / O(√N)" if self.size == 0: self.a = [[x]] self.size = 1 return True a = self._find_bucket(x) i = bisect_left(a, x) if i != len(a) and a[i] == x: return False a.insert(i, x) self.size += 1 if len(a) > len(self.a) * self.REBUILD_RATIO: self._build() return True def _pop(self, a: List[T], i: int) -> T: ans = a.pop(i) self.size -= 1 if not a: self._build() return ans def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) if i == len(a) or a[i] != x: return False self._pop(a, i) return True def lt(self, x: T) -> Optional[T]: "Find the largest element < x, or None if it doesn't exist." for a in reversed(self.a): if a[0] < x: return a[bisect_left(a, x) - 1] def le(self, x: T) -> Optional[T]: "Find the largest element <= x, or None if it doesn't exist." for a in reversed(self.a): if a[0] <= x: return a[bisect_right(a, x) - 1] def gt(self, x: T) -> Optional[T]: "Find the smallest element > x, or None if it doesn't exist." for a in self.a: if a[-1] > x: return a[bisect_right(a, x)] def ge(self, x: T) -> Optional[T]: "Find the smallest element >= x, or None if it doesn't exist." for a in self.a: if a[-1] >= x: return a[bisect_left(a, x)] def __getitem__(self, i: int) -> T: "Return the i-th element." if i < 0: for a in reversed(self.a): i += len(a) if i >= 0: return a[i] else: for a in self.a: if i < len(a): return a[i] i -= len(a) raise IndexError def pop(self, i: int = -1) -> T: "Pop and return the i-th element." if i < 0: for a in reversed(self.a): i += len(a) if i >= 0: return self._pop(a, i) else: for a in self.a: if i < len(a): return self._pop(a, i) i -= len(a) raise IndexError def index(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans class SortedMultiset(Generic[T]): BUCKET_RATIO = 50 REBUILD_RATIO = 170 def _build(self, a: Optional[List[T]] = None) -> None: "Evenly divide `a` into buckets." if a is None: a = list(self) size = self.size = len(a) bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO))) self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)] def __init__(self, a: Iterable[T] = []) -> None: "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)" a = list(a) if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)): a = sorted(a) self._build(a) def __iter__(self) -> Iterator[T]: for i in self.a: for j in i: yield j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __eq__(self, other) -> bool: return list(self) == list(other) def __len__(self) -> int: return self.size def __repr__(self) -> str: return "SortedMultiset" + str(self.a) def __str__(self) -> str: s = str(list(self)) return "{" + s[1 : len(s) - 1] + "}" def _find_bucket(self, x: T) -> List[T]: "Find the bucket which should contain x. self must not be empty." for a in self.a: if x <= a[-1]: return a return a def __contains__(self, x: T) -> bool: if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) return i != len(a) and a[i] == x def count(self, x: T) -> int: "Count the number of x." return self.index_right(x) - self.index(x) def add(self, x: T) -> None: "Add an element. / O(√N)" if self.size == 0: self.a = [[x]] self.size = 1 return a = self._find_bucket(x) insort(a, x) self.size += 1 if len(a) > len(self.a) * self.REBUILD_RATIO: self._build() def _pop(self, a: List[T], i: int) -> T: ans = a.pop(i) self.size -= 1 if not a: self._build() return ans def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) if i == len(a) or a[i] != x: return False self._pop(a, i) return True def lt(self, x: T) -> Optional[T]: "Find the largest element < x, or None if it doesn't exist." for a in reversed(self.a): if a[0] < x: return a[bisect_left(a, x) - 1] def le(self, x: T) -> Optional[T]: "Find the largest element <= x, or None if it doesn't exist." for a in reversed(self.a): if a[0] <= x: return a[bisect_right(a, x) - 1] def gt(self, x: T) -> Optional[T]: "Find the smallest element > x, or None if it doesn't exist." for a in self.a: if a[-1] > x: return a[bisect_right(a, x)] def ge(self, x: T) -> Optional[T]: "Find the smallest element >= x, or None if it doesn't exist." for a in self.a: if a[-1] >= x: return a[bisect_left(a, x)] def __getitem__(self, i: int) -> T: "Return the i-th element." if i < 0: for a in reversed(self.a): i += len(a) if i >= 0: return a[i] else: for a in self.a: if i < len(a): return a[i] i -= len(a) raise IndexError def pop(self, i: int = -1) -> T: "Pop and return the i-th element." if i < 0: for a in reversed(self.a): i += len(a) if i >= 0: return self._pop(a, i) else: for a in self.a: if i < len(a): return self._pop(a, i) i -= len(a) raise IndexError def index(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans class Convex_Hull_Trick: def __init__(self,avl=False): self.avl=avl if self.avl: self.lines=AVLTree_dict() else: self.lines_A=SortedSet() self.lines_B={} def is_removed(self,line0,line1,line2): if line0==None: return False if line2==None: return False a0,b0=line0 a1,b1=line1 a2,b2=line2 return (a1-a0)*(b2-b1)<=(b1-b0)*(a2-a1) def add_line(self,a,b): if self.avl: bb=self.lines[a] else: if a in self.lines_B: bb=self.lines_B[a] else: bb=None if bb!=None and bb<=b: return if self.avl: line0=self.lines.Bisect_Left(a) else: aa=self.lines_A.lt(a) if aa==None: line0=None else: line0=(aa,self.lines_B[aa]) line1=(a,b) if self.avl: line2=self.lines.Bisect_Right(a) else: aa=self.lines_A.gt(a) if aa==None: line2=None else: line2=(aa,self.lines_B[aa]) if self.is_removed(line0,line1,line2): return if self.avl: self.lines[a]=b else: self.lines_A.add(a) self.lines_B[a]=b line2=(a,b) if self.avl: line1=self.lines.Bisect_Left(line2[0]) line0=None if line1==None else self.lines.Bisect_Left(line1[0]) else: aa=self.lines_A.lt(line2[0]) if aa==None: line1=None else: line1=(aa,self.lines_B[aa]) if line1==None: line0=None else: aa=self.lines_A.lt(line1[0]) if aa==None: line0=None else: line0=(aa,self.lines_B[aa]) while self.is_removed(line0,line1,line2): if self.avl: del self.lines[line1[0]] else: assert self.lines_A.discard(line1[0]) del self.lines_B[line1[0]] line1=line0 if self.avl: line0=None if line1==None else self.lines.Bisect_Left(line1[0]) else: aa=self.lines_A.lt(line1[0]) if aa==None: line0=None else: line0=(aa,self.lines_B[aa]) line0=(a,b) if self.avl: line1=self.lines.Bisect_Right(line0[0]) line2=None if line1==None else self.lines.Bisect_Right(line1[0]) else: aa=self.lines_A.gt(line0[0]) if aa==None: line1=None else: line1=(aa,self.lines_B[aa]) if line1==None: line2=None else: aa=self.lines_A.gt(line1[0]) if aa==None: line2=None else: line2=(aa,self.lines_B[aa]) while self.is_removed(line0,line1,line2): if self.avl: del self.lines[line1[0]] else: assert self.lines_A.discard(line1[0]) del self.lines_B[line1[0]] line1=line2 if self.avl: line2=None if line1==None else self.lines.Bisect_Right(line1[0]) else: aa=self.lines_A.gt(line1[0]) if aa==None: line2=None else: line2=(aa,self.lines_B[aa]) def __call__(self,x,y): if self.avl: size=len(self.lines) else: size=len(self.lines_A) if not size: return None ok,ng=-1,size-1 while ng-ok>1: mid=(ok+ng)//2 if self.avl: a0,b0=self.lines.Find_Kth_Element(mid) a1,b1=self.lines.Find_Kth_Element(mid+1) else: a0=self.lines_A[mid] b0=self.lines_B[a0] a1=self.lines_A[mid+1] b1=self.lines_B[a1] if a0*x+b0*y>a1*x+b1*y: ok=mid else: ng=mid if self.avl: a,b=self.lines.Find_Kth_Element(ok+1) else: a=self.lines_A[ok+1] b=self.lines_B[a] return a*x+b*y def __getitem__(self,a): if self.avl: return self.lines[a] else: if a in self.lines_A: return self.lines_B[a] else: return None def __setitem__(self,a,b): self.add_line(a,b) class Cumsum: def __init__(self,lst,mod=0): self.N=len(lst) self.mod=mod self.cumsum=[0]*(self.N+1) self.cumsum[0]=0 for i in range(1,self.N+1): self.cumsum[i]=self.cumsum[i-1]+lst[i-1] if self.mod: self.cumsum[i]%=self.mod def __getitem__(self,i): if type(i)==int: if 0<=i0 if node.bias==1: node.right.bias=-1 node.left.bias=0 elif node.bias==-1: node.right.bias=0 node.left.bias=1 else: node.right.bias=0 node.left.bias=0 node.bias=0 def __getitem__(self,key): v=self.root while v!=None: if keykey: if retu==None or retu[0]>v.key: retu=(v.key,v.value) v=v.left else: v=v.right return retu def Bisect_Left(self,key): retu=None v=self.root while v!=None: if v.key= 2: a1,b1=lines[-2] a2,b2=lines[-1] if (a2-a1)*(b-b2)<(b2-b1)*(a-a2): break lines.pop() lines.append((a, b)) def __call__(self, x,y): lines=self.lines a,b=lines[0] z=a*x+b*y while len(lines) >= 2: a2, b2 = lines[1] z2 = a2 * x + b2*y if z < z2: break z = z2 lines.popleft() return z N=int(readline()) X,Y=[],[] CHT=Convex_Hull_Trick_deque() for n in range(N): x,y=map(int,readline().split()) X.append(x) Y.append(y) for y,x in sorted([(-Y[i],X[i]) for i in range(N)]+[(Y[i],-X[i]) for i in range(N)],reverse=True,key=lambda tpl:tpl[0]): CHT.add_line(y,x) ans=max(-CHT(x,y) for x,y in sorted([(X[i],Y[i]) for i in range(N)]+[(-X[i],-Y[i]) for i in range(N)],key=lambda tpl:tpl[0])) print(ans)