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.*;
  
  public class SolutionD extends Thread {
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new
                                              InputStreamReader(System.in));
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
      }
  
      private static final FastReader scanner = new FastReader();
      private static final PrintWriter out = new PrintWriter(System.out);
  
      public static void main(String[] args) {
          int t = scanner.nextInt();
          for (int i = 0; i < t; i++) {
              solve();
          }
          out.close();
      }
  
      static final long MODULO = 998_244_353;
  
      private static void solve() {
          int n = scanner.nextInt();
  
          long[] pow2 = new long[n+1];
          pow2[0] = 1;
          for (int i = 1; i <= n; i++) {
              pow2[i] = pow2[i-1] * 2;
              if (pow2[i] >= MODULO) {
                  pow2[i] -= MODULO;
              }
          }
  
          int[] a = new int[n];
          int[] distr = new int[n+3];
          for (int i = 0; i < n; i++) {
              a[i] = scanner.nextInt();
              distr[a[i]]++;
          }
  
          long result = pow2[distr[1]]-1; //all non-empty subsequences that only contains 1s.
  
          long[] dp = new long[n+1];
  
          for (int i = 0; i < n; i++) {
              long tmp;
              distr[a[i]]--;
              if (a[i] == 0) {
                  dp[0] = dp[0] * 2 + 1;
                  dp[0] %= MODULO;
                  tmp = pow2[distr[0] + distr[2]]; //all subsequences that have the form 0(0|2)*... and start with index 0
              } else {
                  dp[a[i]] = dp[a[i]] * 2 + dp[a[i]-1];
                  dp[a[i]] %= MODULO;
                  tmp = dp[a[i]-1] * pow2[distr[a[i]] + distr[a[i]+2]]; //all subsequences that have the form (0+)(1+)...(a[i])(a[i]|a[i+2])* and
                  // with the first a[i] at index i
              }
  
              result += tmp;
              result %= MODULO;
          }
  
          System.out.println(result);
      }
  }