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 CPP):

Solution:
#include<bits/stdc++.h>
#define ri register int
#define fi first
#define se second
using namespace std;
inline int read(){
	#define gc getchar
	int ans=0;
	char ch=gc();
	bool f=1;
	while(!isdigit(ch))f^=ch=='-',ch=gc();
	while(isdigit(ch))ans=((ans<<2)+ans<<1)+(ch^48),ch=gc();
	return f?ans:-ans;
	#undef gc
}
typedef long long ll;
typedef pair<int,int> pii;
const int mod=998244353;
inline int add(const int&a,const int&b){return a+b>=mod?a+b-mod:a+b;}
inline int dec(const int&a,const int&b){return a>=b?a-b:a-b+mod;}
inline int mul(const int&a,const int&b){return (ll)a*b%mod;}
inline void Add(int&a,const int&b){a=a+b>=mod?a+b-mod:a+b;}
inline void Dec(int&a,const int&b){a=a>=b?a-b:a-b+mod;}
inline void Mul(int&a,const int&b){a=(ll)a*b%mod;}
inline int ksm(int a,int p){int ret=1;for(;p;p>>=1,a=mul(a,a))if(p&1)Mul(ret,a);return ret;}
const int N=2e5+5;
int n,vx[N],sx=0,vy[N],sy=0,clu[N],cld[N],cru[N],crd[N],pw[N];
pii a[N];
int bit[N];
inline int lowbit(const int&x){return x&-x;}
inline void update(int x,int v){for(;x<=n;x+=lowbit(x))Add(bit[x],v);}
inline int query(int x){int ret=0;for(;x;x-=lowbit(x))Add(ret,bit[x]);return ret;}
inline int query(int l,int r){return dec(query(r),query(l-1));}
int main(){
	n=read();
	pw[0]=1;
	for(ri i=1;i<=n;++i)pw[i]=add(pw[i-1],pw[i-1]);
	for(ri i=1;i<=n;++i){
		vx[i]=a[i].fi=read();
		vy[i]=a[i].se=read();
	}
	sort(vy+1,vy+n+1),sort(a+1,a+n+1);
	for(ri i=1;i<=n;++i){
		a[i].se=lower_bound(vy+1,vy+n+1,a[i].se)-vy;
		clu[i]=query(1,a[i].se-1);
		cld[i]=query(a[i].se+1,n);
		update(a[i].se,1);
	}
	memset(bit,0,sizeof(bit));
	for(ri i=n;i;--i){
		cru[i]=query(1,a[i].se-1);
		crd[i]=query(a[i].se+1,n);
		update(a[i].se,1);
	}
	int ans=0;
	for(ri i=1;i<=n;++i){
		int t=0;
		Add(t,pw[n-1]);
		Add(t,pw[n-1]);
		Dec(t,pw[clu[i]+cld[i]]);
		Dec(t,pw[cru[i]+crd[i]]);
		Dec(t,pw[clu[i]+cru[i]]);
		Dec(t,pw[cld[i]+crd[i]]);
		Add(t,pw[clu[i]]);
		Add(t,pw[cru[i]]);
		Add(t,pw[cld[i]]);
		Add(t,pw[crd[i]]);
		Add(ans,t-1);
	}
	cout<<ans;
	return 0;
}