description: Let's call a sequence of integers x_1, x_2, ..., x_k MEX-correct if for all i (1 ≤ i ≤ k) |x_i - \operatorname{MEX}(x_1, x_2, ..., x_i)| ≤ 1 holds. Where \operatorname{MEX}(x_1, ..., x_k) is the minimum non-negative integer that doesn't belong to the set x_1, ..., x_k. For example, \operatorname{MEX}(1, 0, 1, 3) = 2 and \operatorname{MEX}(2, 1, 5) = 0.
  
  You are given an array a consisting of n non-negative integers. Calculate the number of non-empty MEX-correct subsequences of a given array. The number of subsequences can be very large, so print it modulo 998244353. 
  
  Note: a subsequence of an array a is a sequence [a_{i_1}, a_{i_2}, ..., a_{i_m}] meeting the constraints 1 ≤ i_1 < i_2 < ... < i_m ≤ n. If two different ways to choose the sequence of indices [i_1, i_2, ..., i_m] yield the same subsequence, the resulting subsequence should be counted twice (i. e. two subsequences are different if their sequences of indices [i_1, i_2, ..., i_m] are not the same).
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
  
  The first line of each test case contains a single integer n (1 ≤ n ≤ 5 ⋅ 10^5).
  
  The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ n).
  
  The sum of n over all test cases doesn't exceed 5 ⋅ 10^5.
  
  Output
  
  For each test case, print a single integer — the number of non-empty MEX-correct subsequences of a given array, taken modulo 998244353.
  
  Example
  
  Input
  
  
  4
  3
  0 2 1
  2
  1 0
  5
  0 0 0 0 0
  4
  0 1 2 3
  
  
  Output
  
  
  4
  2
  31
  7
  
  Note
  
  In the first example, the valid subsequences are [0], [1], [0,1] and [0,2].
  
  In the second example, the valid subsequences are [0] and [1].
  
  In the third example, any non-empty subsequence is valid. 
solution: import io
  import os
  from collections import deque
  
  FILE_INPUT_MODE = 0  # 0 for BytesIO, 1 for input.txt, -1 for stdin, input()
  if FILE_INPUT_MODE >= 0:
  
      if FILE_INPUT_MODE == 1:
          CURRENT_DIR = os.path.dirname(os.path.abspath(__file__))
          FD = os.open(f"{CURRENT_DIR}\input.txt", os.O_RDONLY)
      elif FILE_INPUT_MODE == 0:
          FD = 0
      DATA = io.BytesIO(os.read(FD, os.fstat(FD).st_size))
      if FD != 0:
          os.close(FD)
  
      def input():
          return DATA.readline().decode().rstrip('\r\n')
  
  
  def solve():
      p = 998244353
      n = int(input())
      a = [int(word) for word in input().strip().split()]
      mex = [[0, 0] for i in range(max(a) + 2)]
      mex[0][0] = 1
      ans = 0
      for x in a:
          if x - 1 >= 0:
              ans = (ans + mex[x - 1][0] + mex[x - 1][1]) % p
          ans = (ans + mex[x][0]) % p
          ans = (ans + mex[x + 1][0] + mex[x + 1][1]) % p
          if x - 1 >= 0:
              mex[x - 1][1] = (mex[x - 1][1] * 2 + mex[x - 1][0]) % p
          mex[x + 1][0] = (mex[x + 1][0] * 2 + mex[x][0]) % p
          mex[x + 1][1] = mex[x + 1][1] * 2 % p
          # print(mex)
      print(ans)
  
  
  def main():
      t = int(input())
      for _ in range(t):
          solve()
  
  
  if __name__ == "__main__":
      main()
  