Problem: 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.

Examples

Input

3
-1 3
2 1
3 -2


Output

13


Input

4
1 4
2 1
3 3
4 2


Output

34


Input

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


Output

7222

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaynil
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FEnclosedPoints solver = new FEnclosedPoints();
        solver.solve(1, in, out);
        out.close();
    }

    static class FEnclosedPoints {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            node arr[] = new node[n];
            ArrayList<Integer> x = new ArrayList<>();
            ArrayList<Integer> y = new ArrayList<>();
            CustomAVL t = new CustomAVL();
            for (int i = 0; i < n; i++) {
                arr[i] = new node(in.nextInt(), in.nextInt());
                x.add(arr[i].x);
                y.add(arr[i].y);
            }
            Arrays.sort(arr, new Comparator<node>() {

                public int compare(node o1, node o2) {
                    return o1.x - o2.x;
                }
            });
            Collections.sort(x);
            Collections.sort(y);
            long ans = 0;
            long mod = 998244353;
            long twon = Maths.power(2, n, mod);
            for (int i = 0; i < n; i++) {
                int left = Collections.binarySearch(x, arr[i].x);
                int right = n - left - 1;
                int down = Collections.binarySearch(y, arr[i].y);
                int up = n - down - 1;
                int ll = t.getElementsLessThanK(arr[i].y);
                int lr = down - ll;
                int ul = left - ll;
                int ur = up - ul;
//            out.println(left + " " + right + " " + up + " " + down + " " + ll + " " + lr + " " + ur + " " + ul + " ");
                long rc = Maths.power(2, right, mod);
                long lc = Maths.power(2, left, mod);
                long uc = Maths.power(2, up, mod);
                long dc = Maths.power(2, down, mod);
                long llc = Maths.power(2, ll, mod);
                long lrc = Maths.power(2, lr, mod);
                long urc = Maths.power(2, ur, mod);
                long ulc = Maths.power(2, ul, mod);
                ans += (twon - lc - rc - uc - dc + llc + lrc + urc + ulc - 1 + 5 * mod) % mod;
                ans %= mod;
                t.insertElement(arr[i].y);
            }
            out.println(ans);
        }

        class node {
            int x;
            int y;

            node(int x, int y) {
                this.x = x;
                this.y = y;
            }

        }

    }

    static class Maths {
        static long power(long x, long y, long p) {
            long res = 1;
            x = x % p;
            while (y > 0) {
                if ((y & 1) == 1)
                    res = (res * x) % p;
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }

    }

    static class CustomAVL {
        node root;

        CustomAVL() {
            this.root = null;
        }

        public int height(node temp) {
            if (temp == null) {
                return 0;
            } else {
                return temp.height;
            }
        }

        public int getBalance(node temp) {
            if (temp == null) {
                return 0;
            } else {
                return height(temp.left) - height(temp.right);
            }
        }

        public int max(int a, int b) {
            return (a > b) ? a : b;
        }

        public node rightrotate(node y) {
            node x = y.left;
            node T2 = x.right;
            y.lsum = y.lsum - x.lsum;
            y.lcount = y.lcount - x.lcount;
            x.rsum = x.rsum + y.rsum;
            x.rcount = x.rcount + y.rcount;
            x.right = y;
            y.left = T2;
            y.height = max(height(y.left), height(y.right)) + 1;
            x.height = max(height(x.left), height(x.right)) + 1;

            return x;

        }

        public node leftrotate(node x) {
            node y = x.right;
            node T2 = y.left;
            y.lsum = y.lsum + x.lsum;
            y.lcount = y.lcount + x.lcount;
            x.rsum = x.rsum - y.rsum;
            x.rcount = x.rcount - y.rcount;
            y.left = x;
            x.right = T2;
            x.height = max(height(x.left), height(x.right)) + 1;
            y.height = max(height(y.left), height(y.right)) + 1;
            return y;
        }

        public node insert(node root, long value) {
            if (root == null) {
                return new node(value);
            }
            if (value <= root.value) {
                root.lcount = root.lcount + 1;
                root.lsum = root.lsum + value;
                root.left = insert(root.left, value);
            } else {
                root.rsum = root.rsum + value;
                root.rcount = root.rcount + 1;
                root.right = insert(root.right, value);

            }
            root.height = 1 + max(height(root.left), height(root.right));
            int balance = getBalance(root);

            //ll
            if (balance > 1 && value <= root.left.value) {
                return rightrotate(root);
            }
            //rr
            if (balance < -1 && value > root.right.value) {
                return leftrotate(root);
            }
            //lr
            if (balance > 1 && value >= root.left.value) {
                root.left = leftrotate(root.left);
                return rightrotate(root);
            }
            //rl
            if (balance < -1 && value < root.right.value) {
                root.right = rightrotate(root.right);
                return leftrotate(root);
            }
            return root;
        }

        public void insertElement(long value) {
            this.root = insert(root, value);
        }

        public int getElementsLessThanK(long element) {
            node temp = root;
            int rank = 0;
            while (temp != null) {
                if (temp.value == element) {
                    rank += temp.lcount;
                    return rank - 1;
                }
                if (temp.value > element) {
                    temp = temp.left;
                    continue;
                } else {
                    rank += temp.lcount;
                    temp = temp.right;
                    continue;
                }

            }
            return rank;
        }

        class node {
            long value;
            int lcount;
            long lsum;
            long rsum;
            int rcount;
            int height;
            node left;
            node right;

            node(long value) {
                this.value = value;
                this.lcount = 1;
                this.lsum = this.value;
                this.left = null;
                this.right = null;
                this.height = 1;
                this.rsum = this.value;
                this.rcount = 1;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}