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 java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.StringTokenizer;
  
  public class er118d {
  	public static void main(String[] args) {
  		FastScanner scan=new FastScanner();
  		PrintWriter out=new PrintWriter(System.out);
  		
  		int t=scan.nextInt();
  		for(int tt=0;tt<t;tt++) {
  			int n=scan.nextInt();
  			int[] a=new int[n];
  			for(int i=0;i<n;i++) a[i]=scan.nextInt();
  			long[] withTarget=new long[n+10];
  			long[] cantAdvance=new long[n+10];
  			withTarget[0]=1;
  			
  			for(int i=0;i<n;i++) {
  				//we encounter a number x
  				//sequences with target x+1 are doubled (and can carry on)
  				//sequences with target of x will change to sequences with target of x+1
  				//sequences with target x-1 are doubled (but can't carry on)
  				//sequences that can't advance can append one more or one less than target
  				int x=a[i];
  				withTarget[x+1]=add(withTarget[x+1],withTarget[x+1]);
  				withTarget[x+1]=add(withTarget[x+1],withTarget[x]);
  				if(x>0) {
  					cantAdvance[x-1]=mult(cantAdvance[x-1],2);
  					cantAdvance[x-1]=add(cantAdvance[x-1],withTarget[x-1]);
  				}
  				cantAdvance[x+1]=mult(cantAdvance[x+1],2);
  			}
  			long res=0L;
  			for(int i=0;i<=n+1;i++) {
  				res=add(res,withTarget[i]);
  				res=add(res,cantAdvance[i]);
  			}
  			out.println(sub(res,1));//not including empty subsequence
  		}
  		out.close();
  	}
  	public static long add(long a, long b) {
  		return (a+b)%MOD;
  	}
  	public static long sub(long a, long b) {
  		return (a-b+MOD)%MOD;
  	}
  	public static long mult(long a, long b) {
  		return (a*b)%MOD;
  	}
  	static final int MOD=998244353;
  	static class FastScanner {
  		BufferedReader br;
  		StringTokenizer st;
  
  		public FastScanner() {
  			try	{
  				br = new BufferedReader(new InputStreamReader(System.in));
  				st = new StringTokenizer(br.readLine());
  			} catch (Exception e){e.printStackTrace();}
  		}
  
  		public String next() {
  			if (st.hasMoreTokens())	return st.nextToken();
  			try {st = new StringTokenizer(br.readLine());}
  			catch (Exception e) {e.printStackTrace();}
  			return st.nextToken();
  		}
  
  		public int nextInt() {return Integer.parseInt(next());}
  
  		public long nextLong() {return Long.parseLong(next());}
  
  		public double nextDouble() {return Double.parseDouble(next());}
  
  		public String nextLine() {
  			String line = "";
  			if(st.hasMoreTokens()) line = st.nextToken();
  			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
  			while(st.hasMoreTokens()) line += " "+st.nextToken();
  			return line;
  		}
  	}
  }