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:
def f_encolsed_points(MOD=998244353):
    # 参考: https://atcoder.jp/contests/abc136/submissions/6696160
    import sys
    input = sys.stdin.readline

    class BIT(object):
        """Binary Indexed Tree (1-indexed)"""

        def __init__(self, n):
            self.size = n
            self.tree = [0] * (n + 1)

        def sum(self, index):
            """tree[1]からtree[index]までの和を計算"""
            ret = 0
            while index > 0:
                ret += self.tree[index]
                index -= index & (-index)
            return ret

        def add(self, index, value=1):
            """tree[index]にvalueを加算"""
            while index <= self.size:
                self.tree[index] += value
                index += index & (-index)

    N = int(input())
    Pos = [[int(i) for i in input().split()] for j in range(N)]

    Pos.sort()  # x座標でソートする
    _, pos_y = zip(*Pos)
    y_comp = {y: i for i, y in enumerate(sorted(pos_y), 1)}  # y座標を圧縮

    pow_2 = [1]
    for _ in range(N):
        pow_2.append(pow_2[-1] * 2 % MOD)

    ans = 0
    tree = BIT(N)
    # x座標が小さな点から順に考える
    for left, (_x, _y) in enumerate(Pos):
        y = y_comp[_y]

        # それぞれ、注目している点の 右|下|上 にいくつ点が存在するか
        right = N - 1 - left
        down = y - 1
        up = N - 1 - down

        lower_left = tree.sum(y)
        tree.add(y, 1)
        upper_left = left - lower_left
        lower_right = down - lower_left
        upper_right = right - lower_right

        # 包除原理(全体 - 上下左右 + 左上左下右上右下 - それ自体)
        count = (pow_2[N]
                 - (pow_2[up] + pow_2[down] + pow_2[left] + pow_2[right])
                 + (pow_2[upper_left] + pow_2[lower_left] + pow_2[upper_right] + pow_2[lower_right])
                 - 1)
        ans += count
        ans %= MOD
    return ans

print(f_encolsed_points())