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.BufferedWriter;
  import java.io.InputStreamReader;
  import java.io.OutputStreamWriter;
  
  public class Main {
  
  	private static int REM = 998244353;
  	
  	public static void main(String[] args) throws Exception {
  		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
  		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
  		
  		int T = Integer.parseInt(in.readLine());
  		int[] A = new int[500500];
  		long[] dp = new long[500500];
  		int[] prev = new int[500500];
  		int[] total_cnt = new int[500500];
  		int[] current_cnt = new int[500500];
  		int[] P = new int[500500];
  		P[0] = 1;
  		for (int i=1; i<P.length; i++) {
  			P[i] = P[i-1] * 2 % REM;
  		}
  		
  		for (int ts=1; ts<=T; ts++) {
  			int N = Integer.parseInt(in.readLine());
  			
  			int one_count = 0;
  			
  			{
  				int idx = 1;
  				prev[0] = total_cnt[0] = current_cnt[0] = 0;
  				dp[0] = 0;
  				for (int i=1; i<=N; i++) {
  					total_cnt[i] = 0;
  					current_cnt[i] = 0;
  					dp[i] = 0;
  					prev[i] = 0;
  				}
  				for (final String st: in.readLine().split(" ")) {
  					A[idx] = Integer.parseInt(st);
  					total_cnt[A[idx]]++;
  					if (A[idx] == 1) {
  						++one_count;
  					}
  					idx += 1;
  				}
  			}
  			
  			long ans = P[one_count] - 1;
  			
  			for (int i=1; i<=N; i++) {
  				long exactly = dp[prev[A[i]]];
  				dp[i] = (2 * dp[prev[A[i]]]) % REM; // exactly i and at most i
  				if (A[i] > 0) {
  					exactly += dp[prev[A[i]-1]];
  					dp[i] += dp[prev[A[i]-1]];
  				} else {
  					exactly++;
  					dp[i]++;
  				}
  				dp[i] %= REM;
  				exactly %= REM;
  				//out.write(i + " " + dp[i] + "\n");
  				ans += exactly;
  				
  				
  				if (A[i] > 1) {
  					int cnt1 = total_cnt[A[i]] - current_cnt[A[i]];
  					int cnt2 = total_cnt[A[i]-2] - current_cnt[A[i]-2];
  					ans += dp[prev[A[i]-2]] * P[cnt1+cnt2-1] % REM;
  					/*out.write(i + " " + cnt1 + " " + cnt2 + " " +
  									dp[prev[A[i]-2]] + "\n");*/
  				}
  				
  				ans %= REM;
  				current_cnt[A[i]]++;
  				prev[A[i]] = i;
  			}
  			
  			
  			
  			out.write(ans + "\n");
  		}
  		
  		
  		
  		in.close();
  		out.close();
  	}
  
  }
  