output_description: Print the sum of f(T) over all non-empty subset T of S, modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      x_1 y_1
      :
      x_N y_N
attempt: N = int(input())
  point = [list(map(int, input().split())) for i in range(N)]
  
  x = []
  y = []
  for p in point:
      x.append(p[0])
      y.append(p[1])
  
  x.sort()
  y.sort()
  
  x_dict = {}
  y_dict = {}
  
  for i in range(len(x)):
      x_dict[x[i]] = i
  
  for i in range(len(y)):
      y_dict[y[i]] = i
  
problem_description: Statement
  
  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.
samples: [{"input": "3\n    -1 3\n    2 1\n    3 -2", "output": "13\n    \n\nLet the first, second, and third points be P_1, P_2, and P_3, respectively. S\n= \\\\{P_1, P_2, P_3\\\\} has seven non-empty subsets, and f has the following\nvalues for each of them:\n\n  * f(\\\\{P_1\\\\}) = 1\n  * f(\\\\{P_2\\\\}) = 1\n  * f(\\\\{P_3\\\\}) = 1\n  * f(\\\\{P_1, P_2\\\\}) = 2\n  * f(\\\\{P_2, P_3\\\\}) = 2\n  * f(\\\\{P_3, P_1\\\\}) = 3\n  * f(\\\\{P_1, P_2, P_3\\\\}) = 3\n\nThe sum of these is 13.\n\n* * *"}, {"input": "4\n    1 4\n    2 1\n    3 3\n    4 2", "output": "34\n    \n\n* * *"}, {"input": "10\n    19 -11\n    -3 -12\n    5 3\n    3 -15\n    8 -14\n    -9 -20\n    10 -9\n    0 2\n    -7 17\n    6 -6", "output": "7222\n    \n\nBe sure to print the sum modulo 998244353."}]