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 sys, os, io
  
  
  input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
  
  
  def mex_sequences(n, a):
      sequences_by_head = {(0, 1): 0,
                           (1, 0): 0}
  
      heads_by_mex = {0: [(0, 1)],
                      1: [(1, 0)]}
  
      for ai in a:
          new = {}
          mexes = [ai - 1, ai, ai + 1]
          for mex_ in mexes:
              for mex, max in heads_by_mex.get(mex_, []):
                  # if abs(ai - mex) <= 1:
                  if mex < max:
                      if ai != mex:
                          new[(mex, max)] = new.get((mex, max), 0) + sequences_by_head[(mex, max)]
                          if ai == 1:
                              if ai == max:
                                  new[(mex, max)] += 1
                  else:
                      if ai == max:
                          new[(mex, max)] = new.get((mex, max), 0) + sequences_by_head[(mex, max)]
                          if ai == 0:
                              new[(mex, max)] += 1
                      elif ai == mex:
                          add = sequences_by_head[(mex, max)]
                          if add == 0:
                              continue
                          new[(mex + 1, ai)] = new.get((mex + 1, ai), 0) + add
                      elif ai == mex + 1:
                          add = sequences_by_head[(mex, max)]
                          if add == 0:
                              continue
                          new[(mex, ai)] = new.get((mex, ai), 0) + add
  
          for head in new:
              sequences_by_head[head] = (sequences_by_head.get(head, 0) + new[head]) % 998244353
              mex, _ = head
              heads = heads_by_mex.get(mex, [])
              if head in heads:
                  continue
              heads_by_mex[mex] = heads + [head]
  
      total = 0
      for head in sequences_by_head:
          total += sequences_by_head[head]
          total %= 998244353
      return total
  
  
  for _ in range(int(input())):
      n = int(input())
      a = list(map(int, input().split()))
      sys.stdout.write(f"{mex_sequences(n, a)}\n")
  