Problem:
Score : 600 points

Problem Statement

We have a set S of N points in a two-dimensional plane. The coordinates of the i-th point are (x_i, y_i). The N points have distinct x-coordinates and distinct y-coordinates.

For a non-empty subset T of S, let f(T) be the number of points contained in the smallest rectangle, whose sides are parallel to the coordinate axes, that contains all the points in T. More formally, we define f(T) as follows:

f(T) := (the number of integers i (1 \leq i \leq N) such that a \leq x_i \leq b and c \leq y_i \leq d, where a, b, c, and d are the minimum x-coordinate, the maximum x-coordinate, the minimum y-coordinate, and the maximum y-coordinate of the points in T)

Find the sum of f(T) over all non-empty subset T of S. Since it can be enormous, print the sum modulo 998244353.

Constraints

1 \leq N \leq 2 \times 10^5

-10^9 \leq x_i, y_i \leq 10^9

x_i \neq x_j (i \neq j)

y_i \neq y_j (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the sum of f(T) over all non-empty subset T of S, modulo 998244353.

Sample Input 1

3
-1 3
2 1
3 -2

Sample Output 1

13

Let the first, second, and third points be P_1, P_2, and P_3, respectively. S = \{P_1, P_2, P_3\} has seven non-empty subsets, and f has the following values for each of them:

f(\{P_1\}) = 1

f(\{P_2\}) = 1

f(\{P_3\}) = 1

f(\{P_1, P_2\}) = 2

f(\{P_2, P_3\}) = 2

f(\{P_3, P_1\}) = 3

f(\{P_1, P_2, P_3\}) = 3

The sum of these is 13.

Sample Input 2

4
1 4
2 1
3 3
4 2

Sample Output 2

34

Sample Input 3

10
19 -11
-3 -12
5 3
3 -15
8 -14
-9 -20
10 -9
0 2
-7 17
6 -6

Sample Output 3

7222

Be sure to print the sum modulo 998244353.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#if MYDEBUG
#include "lib/cp_debug.hpp"
#else
#define DBG(...) ;
#endif
#if __cplusplus <= 201402L
template <typename T>
T gcd(T a, T b) { return ((a % b == 0) ? b : gcd(b, a % b)); }
template <typename T>
T lcm(T a, T b) { return a / gcd(a, b) * b; }
#endif
using LL = long long;
constexpr LL LINF = 334ll << 53;
constexpr int INF = 15 << 26;
constexpr LL MOD = 998244353;

namespace Problem {
using namespace std;
template <typename T>
struct BIT {
  vector<T> bit;
  int size;
  BIT(int _size) : bit(vector<T>(_size + 1, 0)), size(_size) {}
  void add(int index, T value) {
    for (int i = index + 1; i <= size; i += (i & -i)) bit[i] += value;
  }
  T sum(int a, int b) {  //sum of[a,b)
    return sum(b) - sum(a);
  }
  T sum(int a) {  // sum of[0,a) = sum of bit[0]~bit[a]
    T ret = 0;
    for (int i = a; i > 0; i -= (i & -i)) ret += bit[i];
    return ret;
  }
};

template <long long Mod = MOD>
class Modint {
 public:
  long long v;

  Modint(const Modint &x) { v = x.v; }
  explicit Modint(int x) {
    if (x < 0 or Mod <= x) x %= Mod;
    if (x < 0) x += Mod;
    v = x;
  }
  explicit Modint(long long x) {
    if (x < 0 or Mod <= x) x %= Mod;
    if (x < 0) x += Mod;
    v = x;
  }
  explicit Modint(unsigned x) {
    if (Mod <= x) x %= Mod;
    v = x;
  }
  explicit Modint(unsigned long long x) {
    if (Mod <= x) x %= Mod;
    v = x;
  }
  template <typename T>
  explicit Modint(T x) {
    if (x < 0 or Mod <= x) x %= Mod;
    v = x;
  }
  Modint() : v(0) {}
  long long get() const { return v; }
  Modint mpow(Modint &n) const { return mpow(n.v); }
  Modint mpow(long long n) const {
    long long i = 1, p = v;
    Modint ret(1);
    while (i <= n) {
      if (i & n) ret *= p;
      i = (i << 1);
      p = (p * p) % Mod;
    }
    return ret;
  }
  Modint operator-() const { return (v ? Modint(Mod - v) : Modint(0)); }
  explicit operator int() const { return v; }
  explicit operator long long() const { return v; }
  Modint &operator+=(const Modint &a) {
    v = (v + a.v);
    if (v >= Mod) v -= Mod;
    return *this;
  }
  Modint &operator-=(const Modint &a) {
    v = (v - a.v);
    if (v < 0) v += Mod;
    return *this;
  }
  Modint &operator*=(const Modint &a) {
    v = (v * a.v) % Mod;
    return *this;
  }
  Modint &operator/=(const Modint &a) {
    v = (v * a.mpow(Mod - 2).v) % Mod;
    return *this;
  }
  template <class T>
  Modint &operator+=(const T &a) {
    v = (v + Modint(a).v);
    if (v >= Mod) v -= Mod;
    return *this;
  }
  template <class T>
  Modint &operator-=(const T &a) {
    v = (v - Modint(a).v);
    if (v < 0) v += Mod;
    return *this;
  }
  template <class T>
  Modint &operator*=(const T &a) {
    v = (v * Modint(a).v) % Mod;
    return *this;
  }
  template <class T>
  Modint &operator/=(const T &a) {
    v = (v * Modint(a).mpow(Mod - 2).v) % Mod;
    return *this;
  }
  friend Modint operator+(const Modint &a, const Modint &b) {
    return Modint(a) += b;
  }
  friend Modint operator-(const Modint &a, const Modint &b) {
    return Modint(a) -= b;
  }
  friend Modint operator*(const Modint &a, const Modint &b) {
    return Modint(a) *= b;
  }
  friend Modint operator/(const Modint &a, const Modint &b) {
    return Modint(a) /= b;
  }
  template <class T, class U>
  friend Modint operator+(const T &a, const U &b) {
    return Modint(a) += Modint(b);
  }
  template <class T, class U>
  friend Modint operator-(const T &a, const U &b) {
    return Modint(a) -= Modint(b);
  }
  template <class T, class U>
  friend Modint operator*(const T &a, const U &b) {
    return Modint(a) *= Modint(b);
  }
  template <class T, class U>
  friend Modint operator/(const T &a, const U &b) {
    return Modint(a) /= Modint(b);
  }
};

template <long long M>
ostream &operator<<(ostream &os, const Modint<M> m) {
  return os << m.v;
}
class Solver {
 public:
  int n;
  vector<int> x, y;
  BIT<int> l2r, r2l;
  Solver(LL n) : n(n), x(n), y(n), l2r(n), r2l(n){};

  void solve() {
    for (int i = 0; i < n; ++i) {
      cin >> x[i] >> y[i];
    }
    vector<int> X(x), Y(y);
    sort(X.begin(), X.end());
    X.erase(unique(X.begin(), X.end()), X.end());
    sort(Y.begin(), Y.end());
    Y.erase(unique(Y.begin(), Y.end()), Y.end());
    for (int i = 0; i < n; ++i) {
      x[i] = distance(X.begin(), lower_bound(X.begin(), X.end(), x[i]));
      y[i] = distance(Y.begin(), lower_bound(Y.begin(), Y.end(), y[i]));
    }
    vector<int> ix(n), iy(n);
    for (int i = 0; i < n; ++i) {
      ix[x[i]] = i;
      iy[y[i]] = i;
    }
    vector<int> lu(n), ld(n), ru(n), rd(n);
    for (int i = 0; i < n; ++i) {
      int id = ix[i];
      int yfromid = y[id];
      ld[id] = l2r.sum(yfromid);
      lu[id] = i - ld[id];
      l2r.add(yfromid, 1);
    }
    for (int i = 0; i < n; ++i) {
      int id = ix[n - 1 - i];
      int yfromid = y[id];
      rd[id] = r2l.sum(yfromid);
      ru[id] = i - rd[id];
      r2l.add(yfromid, 1);
    }
    Modint<> ans(0);
    for (int i = 0; i < n; ++i) {
      int l = x[i];
      int r = n - 1 - l;
      int d = y[i];
      int u = n - 1 - d;
      auto two = Modint<>(2);
      Modint<> tmp = two.mpow(n) - 1;
      tmp -= two.mpow(l) + two.mpow(r) + two.mpow(d) + two.mpow(u);
      tmp += two.mpow(ld[i]) + two.mpow(lu[i]) + two.mpow(rd[i]) + two.mpow(ru[i]);
      ans += tmp;
    }
    cout << ans << endl;
  }
};

}  // namespace Problem

int main() {
  std::cin.tie(0);
  std::ios_base::sync_with_stdio(false);
  // std::cout << std::fixed << std::setprecision(12);
  long long n = 0;
  std::cin >> n;

  Problem::Solver sol(n);
  sol.solve();
  return 0;
}