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 FastScanner fs = new FastScanner(System.in);
      static PrintWriter pw = new PrintWriter(System.out);
      static StringBuilder sb = new StringBuilder();
      static int mod = 998244353;
  
      public static void main(String[] args) throws Exception {
          int n = fs.nextInt();
          for(int i = 0; i < n; i++) solve();
          pw.flush();
      }
  
      public static void solve() {
         int n = fs.nextInt();
         long[] dp1 = new long[n + 2];
         long[] dp2 = new long[n + 2];
         dp1[0] = 1;
          for(int i = 0; i < n; i++) {
              int x = fs.nextInt();
              if(x > 0) dp2[x - 1] = (dp1[x - 1] + dp2[x - 1] * 2) % mod;
              // Calculate all subsequence of type 0
              dp1[x + 1] = (dp1[x + 1] * 2 + dp1[x]) % mod;
              // Calculate all subsequence of type 1
              dp2[x + 1] = (2 * dp2[x + 1]) % mod;
          }
          int ans = 1;
          for(int i = 0; i < dp1.length; i++) {
              ans += (dp1[i] + dp2[i]) % mod;
              ans %= mod;
          }
          pw.println((ans + mod - 2) % mod);
      }
  
      static class GeekInteger {
          public static void save_sort(int[] array) {
              shuffle(array);
              Arrays.sort(array);
          }
  
          public static int[] shuffle(int[] array) {
              int n = array.length;
              Random random = new Random();
              for (int i = 0, j; i < n; i++) {
                  j = i + random.nextInt(n - i);
                  int randomElement = array[j];
                  array[j] = array[i];
                  array[i] = randomElement;
              }
              return array;
          }
  
          public static void save_sort(long[] array) {
              shuffle(array);
              Arrays.sort(array);
          }
  
          public static long[] shuffle(long[] array) {
              int n = array.length;
              Random random = new Random();
              for (int i = 0, j; i < n; i++) {
                  j = i + random.nextInt(n - i);
                  long randomElement = array[j];
                  array[j] = array[i];
                  array[i] = randomElement;
              }
              return array;
          }
  
      }
      static class FastScanner {
          private BufferedReader reader = null;
          private StringTokenizer tokenizer = null;
  
          public FastScanner(InputStream in) {
              reader = new BufferedReader(new InputStreamReader(in));
              tokenizer = null;
          }
  
          public FastScanner(FileReader in) {
              reader = new BufferedReader(in);
              tokenizer = null;
          }
  
          public String next() {
              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public String nextLine() {
              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      return reader.readLine();
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken("\n");
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          public String[] nextArray(int n) {
              String[] a = new String[n];
              for (int i = 0; i < n; i++)
                  a[i] = next();
              return a;
          }
  
          public int[] nextIntArray(int n) {
              int[] a = new int[n];
              for (int i = 0; i < n; i++)
                  a[i] = nextInt();
              return a;
          }
  
          public long[] nextLongArray(int n) {
              long[] a = new long[n];
              for (int i = 0; i < n; i++)
                  a[i] = nextLong();
              return a;
          }
      }
  }
  
  
  