import sys from sortedcollections import SortedSet input = sys.stdin.readline # https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py # https://githubplus.com/tatyam-prime/SortedSet 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 import sys input = sys.stdin.buffer.readline sys.setrecursionlimit(10 ** 7) class SegTree(object): def __init__(self, N, op_data, u_data): self._n = N self.log = (N-1).bit_length() self.size = 1 << self.log self.op = op_data self.e = u_data self.data = [u_data] * (2 * self.size) # self.len = [1] * (2 * self.size) def _update(self, i): self.data[i] = self.op(self.data[i << 1], self.data[i << 1 | 1]) def initialize(self, arr=None): """ segtreeをarrで初期化する。len(arr) == Nにすること """ if arr: for i, a in enumerate(arr, self.size): self.data[i] = a for i in reversed(range(1, self.size)): self._update(i) # self.len[i] = self.len[i << 1] + self.len[i << 1 | 1] def update(self, p, x): """ data[p] = x とする (0-indexed)""" p += self.size self.data[p] = x for i in range(1, self.log + 1): self._update(p >> i) def get(self, p): """ data[p]を返す """ return self.data[p + self.size] def prod(self, l, r): """ op_data(data[l], data[l+1], ..., data[r-1])を返す (0-indexed) """ sml = self.e smr = self.e l += self.size r += self.size while l < r: if l & 1: sml = self.op(sml, self.data[l]) l += 1 if r & 1: r -= 1 smr = self.op(self.data[r], smr) l >>= 1 r >>= 1 return self.op(sml, smr) def all_prod(self): """ op(data[0], data[1], ... data[N-1])を返す """ return self.data[1] def max_right(self, l, func): """ func(l, l+1, ..., r-1) = True, func(l, l+1, ..., r-1, r) = Falseとなる r を返す """ if l == self._n: return self._n l += self.size sm = self.e while True: while l % 2 == 0: l >>= 1 if not func(self.op(sm, self.data[l])): while l < self.size: l <<= 1 if func(self.op(sm, self.data[l])): sm = self.op(sm, self.data[l]) l += 1 return l - self.size sm = self.op(sm, self.data[l]) l += 1 if (l & -l) == l: break return self._n def min_left(self, r, func): """ func( l, l+1, ..., r-1) = True, func(l-1, l, l+1, ..., r-1) = Falseとなる l を返す """ if r == 0: return 0 r += self.size sm = self.e while True: r -= 1 while r > 1 and r & 1: r >>= 1 if not func(self.op(self.data[r], sm)): while r < self.size: r = r << 1 | 1 if func(self.op(self.data[r], sm)): sm = self.op(self.data[r], sm) r -= 1 return r + 1 - self.size sm = self.op(self.data[r], sm) if (r & -r) == r: break return 0 class LazySegTree(SegTree): def __init__(self, N, op_data, u_data, op_lazy, u_lazy, op_merge): super().__init__(N, op_data, u_data) self.composition = op_lazy self.mapping = op_merge self.id = u_lazy self.lazy = [u_lazy] * self.size def _all_apply(self, i, F): # self.data[i] = self.mapping(F, self.data[i], self.len[i]) self.data[i] = self.mapping(F, self.data[i]) if i < self.size: self.lazy[i] = self.composition(F, self.lazy[i]) def _push(self, i): self._all_apply(i << 1, self.lazy[i]) self._all_apply(i << 1 | 1, self.lazy[i]) self.lazy[i] = self.id def update(self, p, x): """ data[p] = x とする (0-indexed)""" p += self.size for i in reversed(range(1, self.log + 1)): self._push(p >> i) self.data[p] = x for i in range(1, self.log + 1): self._update(p >> i) def apply(self, p, F): """ data[p]にFを作用させる(data[p] = op_merge(F, data[p])とする, 0-indexed) """ p += self.size for i in reversed(range(1, self.log + 1)): self._push(p >> i) # self.data[p] = self.mapping(F, self.data[p], self.len[p]) self.data[p] = self.mapping(F, self.data[p]) for i in range(1, self.log + 1): self._update(p >> i) def range_apply(self, l, r, F): """ i = l, l+1, ..., r-1 について、Fを作用させる(op_merge(F, data[i]), 0-indexed) """ if l == r: return l += self.size r += self.size for i in reversed(range(1, self.log + 1)): # too->down if ((l >> i) << i) != l: self._push(l >> i) if ((r >> i) << i) != r: self._push((r - 1) >> i) l2, r2 = l, r while l < r: if l & 1: self._all_apply(l, F) l += 1 if r & 1: r -= 1 self._all_apply(r, F) l >>= 1 r >>= 1 l, r = l2, r2 for i in range(1, self.log + 1): if ((l >> i) << i) != l: self._update(l >> i) if ((r >> i) << i) != r: self._update((r - 1) >> i) def get(self, p): """ data[p]を返す """ p += self.size for i in reversed(range(1, self.log + 1)): self._push(p >> i) return self.data[p] def prod(self, l, r): """ op_data(data[l], data[l+1], ..., data[r-1])を返す (0-indexed) l == rの時は単位元u_dataを返す """ if l == r: return self.e l += self.size r += self.size for i in reversed(range(1, self.log + 1)): if ((l >> i) << i) != l: self._push(l >> i) if ((r >> i) << i) != r: self._push(r >> i) sml = self.e smr = self.e while l < r: if l & 1: sml = self.op(sml, self.data[l]) l += 1 if r & 1: r -= 1 smr = self.op(self.data[r], smr) l >>= 1 r >>= 1 return self.op(sml, smr) def max_right(self, l, func): """ func(l, l+1, ..., r-1) = True, func(l, l+1, ..., r-1, r) = Falseとなる r を返す """ if l == self._n: return self._n l += self.size for i in reversed(range(1, self.log + 1)): self._push(l >> i) sm = self.e while True: while l % 2 == 0: l >>= 1 if not func(self.op(sm, self.data[[l]])): while l < self.size: self._push(l) l <<= 1 if func(self.op(sm, self.data[l])): sm = self.op(sm, self.data[l]) l += 1 return l - self.size sm = self.op(sm, self.data[l]) l += 1 if (l & -l) == l: break return self._n def min_left(self, r, func): """ func( l, l+1, ..., r-1) = True, func(l-1, l, l+1, ..., r-1) = Falseとなる l を返す """ if r == 0: return 0 r += self.size for i in reversed(range(1, self.log + 1)): self._push((r - 1) >> i) sm = self.e while True: r -= 1 while r > 1 and r & 1: r >>= 1 if not func(self.op(self.data[r], sm)): while r < self.size: self._push(r) r = r << 1 | 1 if func(self.op(self.data[r], sm)): sm = self.op(self.data[r], sm) r -= 1 return r + 1 - self.size sm = self.op(self.data[r], sm) if (r & -r) == r: break return 0 """ 遅延セグ木(ac-library移植) op_data(d_L, d_R) : d_Lとd_Rの二項演算, dataを返す op_lazy(lz_new, lz_orig) : lz_origにlz_newを作用させる, lazyを返す op_merge(lz, d) : dにlzを作用させる, dataを返す """ import heapq n = int(input()) cd = [[int(i) for i in input().split()] for j in range(n)] st = SortedMultiset() st.add(0) st.add(n) wdt = n dp = [] konp = [] ans = 0 for i in range(n): dp.append(cd[i][0]) if i != 0: konp.append([-cd[i][1],i]) ans += cd[i][0]+cd[i][1] ans -= cd[0][1] heapq.heapify(konp) bv = 10**10 u_data = 0 op_data = max segmax = SegTree(wdt, op_data, u_data) segmax.initialize(dp) u_data = bv op_data = min segmin = SegTree(wdt, op_data, u_data) segmin.initialize(dp) tmp = segmin.prod(0,n) idx = segmin.max_right(0,lambda x: x > tmp) ans += tmp segmin.update(idx,bv) segmax.update(idx,bv) for i in range(n-1): kp,i = heapq.heappop(konp) kp *= -1 bigidx = st.gt(i) smlidx = st.lt(i) if bv != segmax.prod(i,bigidx): tmp = segmin.prod(i,bigidx) segidx = segmin.max_right(i,lambda x: x > tmp) else: tmp = segmin.prod(smlidx,i) segidx = segmin.max_right(smlidx,lambda x: x > tmp) if tmp < kp: st.add(i) segmax.update(segidx,bv) segmin.update(segidx,bv) ans -= (kp-tmp) print(ans)