use std::collections::*; use std::io::Write; type Map = BTreeMap; type Set = BTreeSet; type Deque = VecDeque; fn main() { input! { n: usize, p: [(usize1, usize); n], } let mut z = p.iter().flat_map(|p| [p.0, p.1]).collect::>(); z.sort(); z.dedup(); let mut seg = LazySegmentTree::build( z.windows(2).map(|z| (M::zero(), M::from(z[1] - z[0]))), z.len() - 1, R, ); let mut cnt = M::zero(); let mut all = M::one(); for &(l, r) in p.iter() { all *= M::from(r - l); let s = z.binary_search(&l).unwrap(); let t = z.binary_search(&r).unwrap(); cnt += seg.find(s, t).0 * M::from(r - l).inv(); seg.update(s, t, M::from(r - l).inv()); } let ans = (M::from(n * (n - 1) / 2) - cnt) * M::new(2).inv() * M::fact(n); println!("{}", ans); } struct R; impl TE for R { type T = (M, M); type E = M; fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T { (l.0 + r.0, l.1 + r.1) } fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T { (x.0 + x.1 * *f, x.1) } fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E { *g + *h } fn e(&self) -> Self::T { (M::zero(), M::zero()) } fn id(&self) -> Self::E { M::zero() } } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- // ---------- begin modint ---------- use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub struct ConstantModulo; impl Modulo for ConstantModulo<{ M }> { fn modulo() -> u32 { M } } pub struct ModInt(u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { Self::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut v = self.0 + rhs.0; if v >= T::modulo() { v -= T::modulo(); } Self::new_unchecked(v) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut v = self.0 - rhs.0; if self.0 < rhs.0 { v += T::modulo(); } Self::new_unchecked(v) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; Self::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.is_zero() { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::fmt::Debug for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl Default for ModInt { fn default() -> Self { Self::zero() } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32; if v >= T::modulo() { v -= T::modulo(); } ModInt::new_unchecked(v) } } impl ModInt { pub fn new_unchecked(n: u32) -> Self { ModInt(n, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } pub fn pow(&self, mut n: u64) -> Self { let mut t = Self::one(); let mut s = *self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(&self) -> Self { assert!(!self.is_zero()); self.pow(T::modulo() as u64 - 2) } pub fn fact(n: usize) -> Self { (1..=n).fold(Self::one(), |s, a| s * Self::from(a)) } pub fn perm(n: usize, k: usize) -> Self { if k > n { return Self::zero(); } ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a)) } pub fn binom(n: usize, k: usize) -> Self { if k > n { return Self::zero(); } let k = k.min(n - k); let mut nu = Self::one(); let mut de = Self::one(); for i in 0..k { nu *= Self::from(n - i); de *= Self::from(i + 1); } nu * de.inv() } } // ---------- end modint ---------- // ---------- begin precalc ---------- pub struct Precalc { fact: Vec>, ifact: Vec>, inv: Vec>, } impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..=n { fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32); } ifact[n] = fact[n].inv(); if n > 0 { inv[n] = ifact[n] * fact[n - 1]; } for i in (1..n).rev() { ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32); inv[i] = ifact[i] * fact[i - 1]; } Precalc { fact, ifact, inv } } pub fn inv(&self, n: usize) -> ModInt { assert!(n > 0); self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn perm(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[n - k] } pub fn binom(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end precalc ---------- type M = ModInt>; // ---------- begin Lazy Segment Tree ---------- pub trait TE { type T: Clone; type E: Clone; fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T; fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T; fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E; fn e(&self) -> Self::T; fn id(&self) -> Self::E; } pub struct LazySegmentTree { n: usize, size: usize, bit: u32, op: R, data: Vec<(R::T, R::E)>, } impl LazySegmentTree { pub fn new(n: usize, op: R) -> Self { assert!(n > 0); let size = n.next_power_of_two(); let bit = size.trailing_zeros(); let data = vec![(op.e(), op.id()); 2 * size]; Self { n, size, bit, op, data, } } pub fn build(init: I, n: usize, op: R) -> Self where I: Iterator, { let mut seg = Self::new(n, op); for (data, ini) in seg.data[seg.size..].iter_mut().zip(init) { data.0 = ini; } for i in (1..seg.size).rev() { seg.pull(i); } seg } pub fn update(&mut self, l: usize, r: usize, f: R::E) { assert!(l <= r && r <= self.n); if l == r { return; } self.push_range(l, r); let mut s = l + self.size; let mut t = r + self.size; while s < t { if s & 1 == 1 { self.apply(s, &f); s += 1; } if t & 1 == 1 { t -= 1; self.apply(t, &f); } s >>= 1; t >>= 1; } let l = l + self.size; let r = r + self.size; for k in 1..=self.bit { if (l >> k) << k != l { self.pull(l >> k); } if (r >> k) << k != r { self.pull((r - 1) >> k); } } } pub fn find(&mut self, l: usize, r: usize) -> R::T { assert!(l <= r && r <= self.n); if l == r { return self.op.e(); } self.push_range(l, r); let mut l = l + self.size; let mut r = r + self.size; let mut p = self.op.e(); let mut q = self.op.e(); while l < r { if l & 1 == 1 { p = self.op.fold(&p, &self.data[l].0); l += 1; } if r & 1 == 1 { r -= 1; q = self.op.fold(&self.data[r].0, &q); } l >>= 1; r >>= 1; } self.op.fold(&p, &q) } pub fn set_at(&mut self, x: usize, v: R::T) { assert!(x < self.n); let x = x + self.size; for k in (1..=self.bit).rev() { self.push(x >> k); } self.data[x].0 = v; for k in 1..=self.bit { self.pull(x >> k); } } fn push_range(&mut self, l: usize, r: usize) { let l = l + self.size; let r = r + self.size; for k in (1..=self.bit).rev() { if (l >> k) << k != l { self.push(l >> k); } if (r >> k) << k != r { self.push((r - 1) >> k); } } } fn apply(&mut self, x: usize, f: &R::E) { self.data[x].0 = self.op.eval(&self.data[x].0, f); self.data[x].1 = self.op.merge(&self.data[x].1, f); } fn push(&mut self, x: usize) { let f = std::mem::replace(&mut self.data[x].1, self.op.id()); self.apply(2 * x, &f); self.apply(2 * x + 1, &f); } fn pull(&mut self, x: usize) { self.data[x].0 = self.op.fold(&self.data[2 * x].0, &self.data[2 * x + 1].0); } } // ---------- end Lazy Segment Tree ----------