N=int(input()) A=list(map(int, input().split())) B=list(map(int, input().split())) if N==1: print(0) exit() import sys input = sys.stdin.readline D={} E=[] EE=[] for i in range(N): a,b,c=A[i],B[i],(A[i]+B[i])//2 E.append(a) E.append(b) E.append(c) G=sorted([a,b,c])[::-1] EE.append(G) if a not in D: D[a]=[] if b not in D: D[b]=[] if c not in D: D[c]=[] D[a].append(i) D[b].append(i) D[c].append(i) E=sorted(list(set(E)))[::-1] # https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py import math from bisect import bisect_left, bisect_right, insort from typing import Generic, Iterable, Iterator, TypeVar, Union, List T = TypeVar('T') class SortedMultiset(Generic[T]): BUCKET_RATIO = 50 REBUILD_RATIO = 170 def _build(self, a=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 __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 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 a.pop(i) self.size -= 1 if len(a) == 0: self._build() return True def lt(self, x: T) -> Union[T, None]: "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) -> Union[T, None]: "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) -> Union[T, None]: "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) -> Union[T, None]: "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, x: int) -> T: "Return the x-th element, or IndexError if it doesn't exist." if x < 0: x += self.size if x < 0: raise IndexError for a in self.a: if x < len(a): return a[x] x -= 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 st = SortedMultiset() for i in range(N): st.add((max(A[i],B[i]),i)) M=[1]*N ans=10**10 for e in E: ma=e mi,j=st[0] ans=min(ans,ma-mi) f=0 while st[-1][0]==e: j=st[-1][1] a,b=st[-1] st.discard((a,b)) nex=M[j] if nex==3: print(ans) exit() st.add((EE[j][nex],j)) M[j]+=1