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 os
  import sys
  from io import BytesIO, IOBase
  BUFSIZE = 8192
  class FastIO(IOBase):
      newlines = 0
      def __init__(self, file):
          self._fd = file.fileno()
          self.buffer = BytesIO()
          self.writable = 'x' in file.mode or 'r' not in file.mode
          self.write = self.buffer.write if self.writable else None
      def read(self):
          while True:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              if not b:break
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines = 0
          return self.buffer.read()
      def readline(self):
          while self.newlines == 0:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              self.newlines = b.count(b'\n') + (not b)
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines -= 1
          return self.buffer.readline()
      def flush(self):
          if self.writable:
              os.write(self._fd, self.buffer.getvalue())
              self.buffer.truncate(0), self.buffer.seek(0)
  class IOWrapper(IOBase):
      def __init__(self, file):
          self.buffer = FastIO(file)
          self.flush = self.buffer.flush
          self.writable = self.buffer.writable
          self.write = lambda s: self.buffer.write(s.encode('ascii'))
          self.read = lambda: self.buffer.read().decode('ascii')
          self.readline = lambda: self.buffer.readline().decode('ascii')
  sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
  input = lambda: sys.stdin.readline().rstrip('\r\n')
  
  MOD = 998244353
  
  from collections import defaultdict
  for _ in range(int(input())):
  	n = int(input())
  	a = [*map(int, input().split())]
  	mex_table = defaultdict(lambda:defaultdict(lambda:0))
  	for i in a:
  
  		mtm10 = mex_table[i - 1][i]
  		mtm1p1 = mex_table[i - 1][i + 1]
  		mt0p1 = mex_table[i][i + 1]
  		mtp1p2 = mex_table[i + 1][i + 2]
  		mtp1p3 = mex_table[i + 1][i + 3]
  
  		mex_table[i - 1][i + 1] += mtm10
  		mex_table[i - 1][i + 1] += mtm1p1
  		mex_table[i + 1][i + 2] += mt0p1
  		mex_table[i + 1][i + 2] += mtp1p2
  		mex_table[i + 1][i + 3] += mtp1p3
  
  
  		mex_table[i - 1][i + 1] %= MOD
  		mex_table[i - 1][i + 1] %= MOD
  		mex_table[i + 1][i + 2] %= MOD
  		mex_table[i + 1][i + 2] %= MOD
  		mex_table[i + 1][i + 3] %= MOD
  
  
  		if i == 0:
  			mex_table[1][2] += 1
  			mex_table[1][2] %= MOD
  		elif i == 1:
  			mex_table[0][2] += 1
  			mex_table[0][2] %= MOD
  
  	ans = 0
  	for key in mex_table:
  		for key_2 in mex_table[key]:
  			ans = (ans + mex_table[key][key_2]) % MOD
  	print(ans % MOD)