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 PYTHON3):

Solution:
import sys
stdin = sys.stdin

sys.setrecursionlimit(10 ** 7)

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x) - 1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

class CombTools(object):
    def __init__(self, cap: int, mod: int):
        self.cap = cap
        self.mod = mod
        self.inv = self._calc_inv()
        self.fac = self._calc_fac()
        self.fac_inv = self._calc_fac_inv()

    def _calc_inv(self):
        inv = [0, 1]
        for i in range(2, self.cap+1):
            inv.append((self.mod - (self.mod // i) * inv[self.mod % i]) % self.mod)

        return inv

    def _calc_fac(self):
        fac = [1]
        for i in range(1, self.cap+1):
            fac.append((i * fac[-1]) % self.mod)

        return fac

    def _calc_fac_inv(self):
        fac_inv = [1]
        for i in range(1, self.cap+1):
            fac_inv.append((self.inv[i] * fac_inv[-1]) % self.mod)

        return fac_inv

    def nCr(self, n: int, r: int):
        # validation
        if r > n:
            raise ValueError("n must be larger than r (n={}, r={})".format(n, r))

        # calculation
        return self.fac[n] * self.fac_inv[n-r] * self.fac_inv[r] % self.mod


class BIT(object):
    def __init__(self, n: int):
        self.bitree = [0]*(pow(2, (n-1).bit_length()) + 1)
        self.size = len(self.bitree) - 1

    def add(self, index, value):
        while index <= self.size:
            self.bitree[index] += value
            index += (-index) & index

    def get(self, index):
        ans = 0
        while index > 0:
            ans += self.bitree[index]
            index -= (-index) & index

        return ans


# 入力
n = ni()
xs = []
ys = []
ps = []
MOD = 998244353
for _ in range(n):
    xi, yi = li()
    xs.append(xi)
    ys.append(yi)
    ps.append([xi, yi])

# 座標圧縮
xcomp = {xi: i+1 for i, xi in enumerate(sorted(xs))}
ycomp = {yi: i+1 for i, yi in enumerate(sorted(ys))}
pcomp = [[xcomp[xi], ycomp[yi]] for xi, yi in zip(xs, ys)]
pcomp.sort()

# 答え
ans = 0

# 自分が選択される
ct = CombTools(n, MOD)
for i in range(1,n+1):
    ans += i * ct.nCr(n, i)
    ans %= MOD

# BITで左右管理
leftBIT = BIT(n)
rightBIT = BIT(n)

for _, yi in pcomp:
    rightBIT.add(yi, 1)

# 左端から繰り返し
pow2 = [pow(2, i, MOD) for i in range(n+1)]
for _, yi in pcomp:
    rightBIT.add(yi, -1)

    nw = leftBIT.get(n) - leftBIT.get(yi)
    ne = rightBIT.get(n) - rightBIT.get(yi)
    sw = leftBIT.get(yi)
    se = rightBIT.get(yi)

    ans += (pow2[nw] - 1) * (pow2[se] - 1) * (pow2[ne] * pow2[sw])
    ans += (pow2[sw] - 1) * (pow2[ne] - 1) * (pow2[se] * pow2[nw])
    ans -= (pow2[nw] - 1) * (pow2[ne] - 1) * (pow2[sw] - 1) * (pow2[se] - 1)
    ans %= MOD

    leftBIT.add(yi, 1)

print(ans)