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: from sys import stdin, stdout
  
  mod = 998244353
  
  def pow_mod(x, y):
      if y == 1:
          return x % mod 
  
      half_res = pow_mod(x, y // 2)
      result = half_res * half_res
      if y % 2 == 1:
          result *= x
  
      return result % mod 
  
  t = int(stdin.readline())
  for tt in range(t):
      n = int(stdin.readline())
      a = [int(s) for s in stdin.readline().split()]
  
      ones = 0
      mx = 0
      for i in range(n):
          if a[i] == 1:
              ones += 1
          if a[i] > mx:
              mx = a[i]
  
      sm = pow_mod(2, ones) - 1 if ones > 0 else 0
  
      # print(sm, '~~~')
  
      ending_to = [0 for i in range(mx + 1)]
      done_to = [0 for i in range(mx + 1)]
  
      for i in range(n):
          ending_to[a[i]] *= 2
          if a[i] != 0:
              ending_to[a[i]] += ending_to[a[i] - 1]
          else:
              ending_to[a[i]] += 1
          ending_to[a[i]] %= mod
  
          if a[i] >= 2:
              done_to[a[i] - 1] *= 2
              done_to[a[i] - 1] += ending_to[a[i] - 2]
              done_to[a[i] - 1] %= mod
  
          if a[i] <= mx - 1 and done_to[a[i] + 1] > 0:
              done_to[a[i] + 1] *= 2
              # done_to[a[i] + 1] += ending_to[a[i] - 1] if a[i] > 0 else 0
              done_to[a[i] + 1] %= mod
  
      # for i in range(mx + 1):
      #     print(i, ending_to[i], '!')
      #     print(i, done_to[i], '!!')
  
      for i in range(mx + 1):
          sm = (sm + ending_to[i] + done_to[i]) % mod
  
      sm %= mod
  
      stdout.write(str(sm) + '\n')