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.util.*;
  import java.io.*;
   
  public class D {
  	
  	static final long MOD = 998244353;
   
  	public static void main(String[] args) {
  		FastScanner fs = new FastScanner();
  		PrintWriter pw = new PrintWriter(System.out);
  		StringBuilder sb = new StringBuilder("");
  		int t = fs.nextInt();
  		for (int tt = 1; tt <= t; tt++) {
  			int n = fs.nextInt();
  			int[] a = fs.readArray(n);
  			long[] dp1 = new long[n + 2];
  			long[] dp2 = new long[n + 2];
  			dp1[0] = 1;
  			for (int i = 0; i < n; i++) {
  				dp1[a[i] + 1] = (2 * dp1[a[i] + 1] + dp1[a[i]]) % MOD;
  				if (a[i] > 0) dp2[a[i] - 1] = (2 * dp2[a[i] - 1] + dp1[a[i] - 1]) % MOD;
  				dp2[a[i] + 1] = (2 * dp2[a[i] + 1]) % MOD;
  			}
  			long ans = MOD - 1;
  			for (long x : dp1) ans = (ans + x) % MOD;
  			for (long x : dp2) ans = (ans + x) % MOD;
  			sb.append(ans + "\n");
  		}
  		pw.print(sb.toString());
  		pw.close();
  	}
   
  	static class FastScanner {
  		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  		StringTokenizer st = new StringTokenizer("");
  		String next() {while (!st.hasMoreTokens())try {st = new StringTokenizer(br.readLine());} catch (IOException e) {}return st.nextToken();}
  		int nextInt() {return Integer.parseInt(next());}
  		long nextLong() {return Long.parseLong(next());}
  		double nextDouble() {return Double.parseDouble(next());}
  		int[] readArray(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) {a[i] = nextInt();} return a;}
  	}
  }