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, setrecursionlimit
  from math import gcd, sqrt, factorial, pi, inf
  from collections import deque, defaultdict
  from bisect import bisect, bisect_left
  from time import time
  from itertools import permutations as per
  from heapq import heapify, heappush, heappop, heappushpop
  
  input = stdin.readline
  R = lambda: map(int, input().split())
  I = lambda: int(input())
  S = lambda: input().rstrip('\r\n')
  L = lambda: list(R())
  P = lambda x: stdout.write(str(x) + '\n')
  lcm = lambda x, y: (x * y) // gcd(x, y)
  nCr = lambda x, y: (f[x] * inv((f[y] * f[x - y]) % N)) % N
  inv = lambda x: pow(x, N - 2, N)
  sumx = lambda x: (x ** 2 + x) // 2
  N = 10 ** 9 + 7
  
  mod=998244353
  for _ in range(I()):
      n=I()
      dp1=[0]*(n+2)
      dp2=[0]*(n+2)
      dp1[0]=1
      for i in R():
          dp1[i+1]=(dp1[i+1]<<1)%mod
          dp1[i+1]=(dp1[i+1]+dp1[i])%mod
          if i>0:
              dp2[i-1]=(dp2[i-1]<<1)%mod
              dp2[i-1]=(dp2[i-1]+dp1[i-1])%mod
          dp2[i+1]=(dp2[i+1]<<1)%mod
      ans=0
      for i in range(n+2):
          ans=(ans+dp1[i]+dp2[i])%mod
      print((ans-1)%mod)
  