import math from bisect import bisect_left, bisect_right from typing import Generic, Iterable, Iterator, TypeVar, Union, List T = TypeVar('T') class SortedSet(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 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 __len__(self) -> int: return self.size 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 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 class RangeSet: def __init__(self): self.ss = SortedSet() self.ss.add((INF*2, INF)) def merge(self, l: int, r: int) -> tuple[int, int]: t = self.ss.ge((l, -1)) assert t is not None sr, sl = t # [sl, sr) if r < sl: self.ss.add((r, l)) return l, r if sl <= l and r <= sr: return sl, sr self.ss.discard(t) start = min(l, sl) if r <= sr: self.ss.add((sr, start)) return start, sr return self.merge(start, r) INF = 1 << 60 D, Q = map(int, input().split()) rset = RangeSet() ans = 0 for _ in range(Q): A, B = map(int, input().split()) l, r = rset.merge(A, B+1) ans = max(ans, r-l) #print(f'{A=} {B=}') #print(f' {l=} {r=}') print(ans)