#ifndef LOCAL #define FAST_IO #endif // ============ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; // ============ #ifdef DEBUGF #else #define DBG(x) (void)0 #endif // ============ #include #include #include // ============ constexpr bool is_prime(unsigned n) { if (n == 0 || n == 1) { return false; } for (unsigned i = 2; i * i <= n; ++i) { if (n % i == 0) { return false; } } return true; } constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) { unsigned ret = 1, self = x; while (y != 0) { if (y & 1) { ret = (unsigned) ((unsigned long long) ret * self % mod); } self = (unsigned) ((unsigned long long) self * self % mod); y /= 2; } return ret; } template constexpr unsigned primitive_root() { static_assert(is_prime(mod), "`mod` must be a prime number."); if (mod == 2) { return 1; } unsigned primes[32] = {}; int it = 0; { unsigned m = mod - 1; for (unsigned i = 2; i * i <= m; ++i) { if (m % i == 0) { primes[it++] = i; while (m % i == 0) { m /= i; } } } if (m != 1) { primes[it++] = m; } } for (unsigned i = 2; i < mod; ++i) { bool ok = true; for (int j = 0; j < it; ++j) { if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) { ok = false; break; } } if (ok) return i; } return 0; } // y >= 1 template constexpr T safe_mod(T x, T y) { x %= y; if (x < 0) { x += y; } return x; } // y != 0 template constexpr T floor_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return x / y; } else { return -((-x + y - 1) / y); } } // y != 0 template constexpr T ceil_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return (x + y - 1) / y; } else { return -(-x / y); } } // ============ template class ModInt { static_assert(mod != 0, "`mod` must not be equal to 0."); static_assert( mod < (1u << 31), "`mod` must be less than (1u << 31) = 2147483648."); unsigned val; public: static constexpr unsigned get_mod() { return mod; } constexpr ModInt() : val(0) {} template > * = nullptr> constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {} template > * = nullptr> constexpr ModInt(T x) : val((unsigned) (x % mod)) {} static constexpr ModInt raw(unsigned x) { ModInt ret; ret.val = x; return ret; } constexpr unsigned get_val() const { return val; } constexpr ModInt operator+() const { return *this; } constexpr ModInt operator-() const { return ModInt(0u) - *this; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if (val >= mod) val -= mod; return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { if (val < rhs.val) val += mod; val -= rhs.val; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { val = (unsigned long long)val * rhs.inv().val % mod; return *this; } friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) += rhs; } friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) /= rhs; } constexpr ModInt pow(unsigned long long x) const { ModInt ret = ModInt::raw(1); ModInt self = *this; while (x != 0) { if (x & 1) ret *= self; self *= self; x >>= 1; } return ret; } constexpr ModInt inv() const { static_assert(is_prime(mod), "`mod` must be a prime number."); assert(val != 0); return this->pow(mod - 2); } friend std::istream &operator>>(std::istream &is, ModInt &x) { long long val; is >> val; x.val = val % mod + (val < 0 ? mod : 0); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } friend bool operator==(const ModInt &lhs, const ModInt &rhs) { return lhs.val == rhs.val; } friend bool operator!=(const ModInt &lhs, const ModInt &rhs) { return lhs.val != rhs.val; } }; [[maybe_unused]] constexpr unsigned mod998244353 = 998244353; [[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007; // ============ // ============ // ============ #include #include // ============ #include #include template struct Add { using Value = T; static Value id() { return T(0); } static Value op(const Value &lhs, const Value &rhs) { return lhs + rhs; } static Value inv(const Value &x) { return -x; } }; template struct Mul { using Value = T; static Value id() { return Value(1); } static Value op(const Value &lhs, const Value &rhs) { return lhs * rhs; } static Value inv(const Value &x) { return Value(1) / x; } }; template struct Min { using Value = T; static Value id() { return std::numeric_limits::max(); } static Value op(const Value &lhs, const Value &rhs) { return std::min(lhs, rhs); } }; template struct Max { using Value = T; static Value id() { return std::numeric_limits::min(); } static Value op(const Value &lhs, const Value &rhs) { return std::max(lhs, rhs); } }; template struct Xor { using Value = T; static Value id() { return T(0); } static Value op(const Value &lhs, const Value &rhs) { return lhs ^ rhs; } static Value inv(const Value &x) { return x; } }; template struct Reversible { using Value = std::pair; static Value id() { return Value(Monoid::id(), Monoid::id()); } static Value op(const Value &v1, const Value &v2) { return Value( Monoid::op(v1.first, v2.first), Monoid::op(v2.second, v1.second)); } }; // ============ template class FenwickTree { public: using Value = typename CommutativeGroup::Value; private: std::vector data; public: FenwickTree(int n) : data(n, CommutativeGroup::id()) {} void add(int idx, const Value &x) { assert(idx >= 0 && idx < (int) data.size()); for (; idx < (int) data.size(); idx |= idx + 1) { data[idx] = CommutativeGroup::op(data[idx], x); } } Value sum(int r) const { assert(r >= 0 && r <= (int) data.size()); Value ret = CommutativeGroup::id(); for (; r > 0; r &= r - 1) { ret = CommutativeGroup::op(ret, data[r - 1]); } return ret; } Value sum(int l, int r) const { assert(l >= 0 && l <= r && r <= (int) data.size()); return CommutativeGroup::op(sum(r), CommutativeGroup::inv(sum(l))); } }; template using FenwickTreeAdd = FenwickTree>; // ============ template class RangeAddRangeSum { int n; FenwickTree> ft0; FenwickTree> ft1; public: RangeAddRangeSum(int n) : n(n), ft0(n + 1), ft1(n + 1) {} void add(int l, int r, const T &v) { assert(0 <= l && l <= r && r <= n); ft0.add(l, v); ft0.add(r, -v); ft1.add(l, -T(l) * v); ft1.add(r, T(r) * v); } T sum(int l, int r) const { assert(0 <= l && l <= r && r <= n); return T(r) * ft0.sum(r) + ft1.sum(r) - T(l) * ft0.sum(l) - ft1.sum(l); } }; // ============ // ============ #include #include template class CoordinateCompression { std::vector data; int size_sum() { return 0; } template int size_sum(const std::vector &head, const Tail &...tail) { return (int) head.size() + size_sum(tail...); } void push() {} template void push(const std::vector &head, const Tail &...tail) { for (const T &ele : head) { data.emplace_back(ele); } push(tail...); } void compress() {} template void compress(std::vector &head, Tail &...tail) { for (T &ele : head) { ele = (T) (std::lower_bound(data.begin(), data.end(), ele) - data.begin()); } compress(tail...); } public: template CoordinateCompression(V &...v) { data.reserve(size_sum(v...)); push(v...); std::sort(data.begin(), data.end()); data.erase(std::unique(data.begin(), data.end()), data.end()); compress(v...); } const T &operator[](const T &ele) const { return data[ele]; } int size() const { return data.size(); } bool contains(const T &ele) const { auto it = std::lower_bound(data.begin(), data.end(), ele); return it != data.end() && *it == ele; } T cc(const T &ele) const { return (T) (std::lower_bound(data.begin(), data.end(), ele) - data.begin()); } }; // ============ using Mint = ModInt; int main() { i32 n; cin >> n; Vec b(n), c(n); REP(i, n) { cin >> b[i] >> c[i]; --b[i]; } if (n == 1) { cout << 0 << '\n'; exit(0); } CoordinateCompression cc(b, c); RangeAddRangeSum rr(cc.size()); REP(i, n) { rr.add(b[i], c[i], Mint(1) / Mint(cc[c[i]] - cc[b[i]])); } REP(i, cc.size() - 1) { Mint t = rr.sum(i, i + 1); rr.add(i, i + 1, t * (Mint(cc[i + 1] - cc[i] - 1))); } Mint eq; REP(i, n) { Mint s = rr.sum(b[i], c[i]); DBG(s); s -= Mint(1); s /= Mint(cc[c[i]] - cc[b[i]]); s /= Mint(n) * Mint(n - 1); eq += s; } Mint inv = (Mint(1) - eq) / Mint(2); Mint ex = inv * Mint(n) * Mint(n - 1) / Mint(2); REP(i, 1, n + 1) { ex *= Mint(i); } cout << ex << '\n'; }