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.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    // static int mod = 1_000_000_007;
    int mod = 998244353;
    // long inf = Long.MAX_VALUE/2;
    int inf = Integer.MAX_VALUE/2;

    void solve(){
        int n = ni();
        int[][] board = new int[n][4];
        for(int i = 0; i < n; i++){
            board[i][0] = ni();
            board[i][1] = ni();
        }
        Arrays.sort(board, (a,b)->(a[0]-b[0]));
        for(int i = 0; i < n; i++){
            board[i][2] = i;
        }
        Arrays.sort(board, (a,b)->(a[1]-b[1]));
        for(int i = 0; i < n; i++){
            board[i][3] = i;
        }
        Arrays.sort(board, (a,b)->(a[2]-b[2]));
        BIT left = new BIT(n);
        BIT right = new BIT(n);
        for(int i = 0; i < n; i++){
            right.accumulate(i,1);
        }
        long ans = pow(2,n-1,mod) * n % mod;
        for(int i = 0; i < n; i++){
            right.accumulate(board[i][3], -1);
            long ld = left.sum(0,board[i][3]);
            long lu = left.sum(board[i][3]+1,n);
            long rd = right.sum(0,board[i][3]);
            long ru = right.sum(board[i][3]+1,n);
            long sum = 0;
            sum += pow(2,ld+lu,mod);
            sum += pow(2,ld+rd,mod);
            sum += pow(2,ru+rd,mod);
            sum += pow(2,ru+lu,mod);
            sum -= pow(2,ld,mod);
            sum -= pow(2,lu,mod);
            sum -= pow(2,rd,mod);
            sum -= pow(2,ru,mod);
            long total = (mod+(pow(2,n-1,mod) - sum-1)%mod)%mod;
            // out.println(sum+" "+total);
            ans += total;
            ans %= mod;
            left.accumulate(board[i][3],1);
        }
        out.println(ans);

    }

    private long pow(long a, long n, long MOD) {
        a %= MOD;
        if (a == 0) {
            return 0;
        }

        long loop = n;
        long ret = 1;
        long x = a;
        while (loop > 0) {
            if (loop % 2 == 1) {
                ret = ret * x % MOD;
            }
            x = x * x % MOD;
            loop /= 2;
        }

        return ret;
    }

    class BIT {
        private int n;
        private long[] bit;
        public BIT(int n) {
            this.n = n;
            bit = new long[n+1];
        }

        public void accumulate(int index,long num) {
            index++;
            while(index<=n) {
                bit[index] += num;
                index+=index&-index;
            }
        }

        /* [begin , end) */
        public long sum(int begin,int end) {
            return sum(end) - sum(begin);
        }

        private long sum(int i) {
            long s = 0;
            while(i>0) {
                s+=bit[i];
                i-=i&-i;
            }
            return s;
        }

        public long get(int index) {
            return sum(index,index+1);
        }

        // public void set(int index,long num) {
        //     accumulate(index,num-(sum(index)-sum(index-1)));
        // }

        public String toString() {
            long[] value = new long[n];
            for(int i=0;i<n;i++) {
                value[i] = get(i);
            }
            return Arrays.toString(value);
        }
    }

    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}