Buggy python submission (verdict: Time Limit Exceeded):
MOD = 998244353
import bisect
N = int(input())
P = [list(map(int,input().split())) for i in [0]*N]

class SegmentTree:
    def __init__(self,data):
        N = len(data)
        self.l = 2**((N-1).bit_length())
        self.data = [0]*self.l + data + [0]*(self.l-N)
        for i in range(self.l-1,0,-1):
            self.data[i] = self.data[2*i] + self.data[2*i+1]

    def set(self,i,val):
        i += self.l
        self.data[i] = val
        i = i//2
        while i > 0:
            self.data[i] = self.data[2*i] + self.data[2*i+1]
            i = i//2

    def get(self,i,j):
        i += self.l
        j += self.l
        s = 0
        while j-i > 0:
            if i & 1:
                s += self.data[i]
                i += 1
            if j & 1:
                s += self.data[j-1]
                j -= 1
            i = i//2
            j = j//2
        return s

X,Y = map(list,zip(*P))
X.sort()
Y.sort()
compY = {y:cy for cy,y in enumerate(Y)}
Psorted = sorted(P)
compP = [[n,compY[y]] for n,(_,y) in enumerate(Psorted)]

n1s = []
seg = SegmentTree([0]*N)
for _,y in compP[::-1]:
    n1s.append(seg.get(y,N))
    seg.set(y,1)
n1s = n1s[::-1]

pows = [1]
for i in range(1,N):
    pows.append((pows[-1]*2) % MOD)

ans = (-4*sum(pows)- N + N * pow(2,N,MOD)) % MOD

for n,(x,y) in enumerate(Psorted):
    lower = bisect.bisect_left(Y,y)
    upper = N-1-lower
    left = n
    right = N-n-1
    n1 = n1s[n]
    n2 = upper - n1
    n3 = left - n2
    n4 = right - n1
    ans += pows[n1] + pows[n2] + pows[n3] + pows[n4]
    ans %= MOD

print(ans)


Fixed submission:
MOD = 998244353
import bisect
import sys
input = sys.stdin.readline
N = int(input())
P = [list(map(int,input().split())) for i in [0]*N]

class SegmentTree:
    def __init__(self,data):
        N = len(data)
        self.l = 2**((N-1).bit_length())
        self.data = [0]*self.l + data + [0]*(self.l-N)
        for i in range(self.l-1,0,-1):
            self.data[i] = self.data[2*i] + self.data[2*i+1]

    def set(self,i,val):
        i += self.l
        self.data[i] = val
        i = i//2
        while i > 0:
            self.data[i] = self.data[2*i] + self.data[2*i+1]
            i = i//2

    def get(self,i,j):
        i += self.l
        j += self.l
        s = 0
        while j-i > 0:
            if i & 1:
                s += self.data[i]
                i += 1
            if j & 1:
                s += self.data[j-1]
                j -= 1
            i = i//2
            j = j//2
        return s

X,Y = map(list,zip(*P))
X.sort()
Y.sort()
compY = {y:cy for cy,y in enumerate(Y)}
Psorted = sorted(P)
compP = [[n,compY[y]] for n,(_,y) in enumerate(Psorted)]

n1s = []
seg = SegmentTree([0]*N)
for _,y in compP[::-1]:
    n1s.append(seg.get(y,N))
    seg.set(y,1)
n1s = n1s[::-1]

pows = [1]
for i in range(1,N):
    pows.append((pows[-1]*2) % MOD)

ans = (-4*sum(pows)- N + N * pow(2,N,MOD)) % MOD

for n,(x,y) in enumerate(Psorted):
    lower = bisect.bisect_left(Y,y)
    upper = N-1-lower
    left = n
    right = N-n-1
    n1 = n1s[n]
    n2 = upper - n1
    n3 = left - n2
    n4 = right - n1
    ans += pows[n1] + pows[n2] + pows[n3] + pows[n4]
    ans %= MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
MOD = 998244353
import bisect
N = int(input())
P = [list(map(int,input().split())) for i in [0]*N]
class SegmentTree:
    def __init__(self,data):
        N = len(data)
        self.l = 2**((N-1).bit_length())
        self.data = [0]*self.l + data + [0]*(self.l-N)
        for i in range(self.l-1,0,-1):
            self.data[i] = self.data[2*i] + self.data[2*i+1]

    def set(self,i,val):
        i += self.l
        self.data[i] = val
        i = i//2
        while i > 0:
            self.data[i] = self.data[2*i] + self.data[2*i+1]
            i = i//2

    def get(self,i,j):
        i += self.l
        j += self.l
        s = 0
        while j-i > 0:
            if i & 1:
                s += self.data[i]
                i += 1
            if j & 1:
                s += self.data[j-1]
                j -= 1
            i = i//2
            j = j//2
        return s

X,Y = map(list,zip(*P))
X.sort()
Y.sort()
compY = {y:cp for cp,y in enumerate(Y)}
Psorted = sorted(P)
compP = [[n,compY[y]] for n,(_,y) in enumerate(Psorted)]

n1s = []
seg = SegmentTree([0]*N)
for _,y in compP[::-1]:
    n1s.append(seg.get(y,N))
    seg.set(y,1)
n1s = n1s[::-1]

ans = 0
for n,(x,y) in enumerate(Psorted):
    lower = bisect.bisect_left(Y,y)
    upper = N-1-lower
    left = n
    right = N-n-1
    n1 = n1s[n]
    n2 = upper - n1
    n3 = left - n2
    n4 = right - n1
    temp = pow(2,lower,MOD) + pow(2,upper,MOD) + pow(2,left,MOD) + pow(2,right,MOD)
    temp -= pow(2,n1,MOD)+pow(2,n2,MOD)+pow(2,n3,MOD)+pow(2,n4,MOD)
    temp += 1 # empty
    ans += pow(2,N,MOD) - temp
    ans %= MOD

print(ans)


Fixed submission:
MOD = 998244353
import bisect
import sys
input = sys.stdin.readline
N = int(input())
P = [list(map(int,input().split())) for i in [0]*N]

class SegmentTree:
    def __init__(self,data):
        N = len(data)
        self.l = 2**((N-1).bit_length())
        self.data = [0]*self.l + data + [0]*(self.l-N)
        for i in range(self.l-1,0,-1):
            self.data[i] = self.data[2*i] + self.data[2*i+1]

    def set(self,i,val):
        i += self.l
        self.data[i] = val
        i = i//2
        while i > 0:
            self.data[i] = self.data[2*i] + self.data[2*i+1]
            i = i//2

    def get(self,i,j):
        i += self.l
        j += self.l
        s = 0
        while j-i > 0:
            if i & 1:
                s += self.data[i]
                i += 1
            if j & 1:
                s += self.data[j-1]
                j -= 1
            i = i//2
            j = j//2
        return s

X,Y = map(list,zip(*P))
X.sort()
Y.sort()
compY = {y:cy for cy,y in enumerate(Y)}
Psorted = sorted(P)
compP = [[n,compY[y]] for n,(_,y) in enumerate(Psorted)]

n1s = []
seg = SegmentTree([0]*N)
for _,y in compP[::-1]:
    n1s.append(seg.get(y,N))
    seg.set(y,1)
n1s = n1s[::-1]

pows = [1]
for i in range(1,N):
    pows.append((pows[-1]*2) % MOD)

ans = (-4*sum(pows)- N + N * pow(2,N,MOD)) % MOD

for n,(x,y) in enumerate(Psorted):
    lower = bisect.bisect_left(Y,y)
    upper = N-1-lower
    left = n
    right = N-n-1
    n1 = n1s[n]
    n2 = upper - n1
    n3 = left - n2
    n4 = right - n1
    ans += pows[n1] + pows[n2] + pows[n3] + pows[n4]
    ans %= MOD

print(ans)