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.*;
  import java.util.*;
  
  public class D {
      /**
       * Valid MEX sequence:
       *  A. 0..0 1..1 2..2 x-1..x-1 x..x
       *  B. 0..0 1..1 2..2 x-1..x-1 x+1..x+1 x-1..x-1
       *
       * state:
       *  dp1[i][j] denotes # sequences on type A on prefix of length i with MEX equal to j
       *  dp2[i][j] denotes # sequences on type B on prefix of length i with MEX equal to j
       * transition:
       *  0 1 2 3    +4   x == j
       *  0 1 2 3     3   x == j - 1
       *  0 1 2 3     5   x == j + 1
       *  pre: dp[i - 1][j]
       *  if x == j - 1 dp1[i - 1][j] -> dp1[i][j]
       *  if x == j     dp1[i - 1][j] -> dp1[i][j + 1]
       *  if x == j + 1 dp1[i - 1][j] -> dp2[i][j]
       *  0 1 2 4 +2/4
       *  if x == j - 1 dp2[i - 1][j] -> dp2[i][j]
       *  if x == j + 1 dp2[i - 1][j] -> dp2[i][j]
       * */
      private static final int MOD = 998244353;
      void go() {
          // add code
          int n = Reader.nextInt();
          int ans = -1;
  
          int[] dp1 = new int[n + 2];
          int[] dp2 = new int[n + 2];
  
          dp1[0] = 1;
  
          for(int i = 1; i <= n; i++) {
              int x = Reader.nextInt();
  
              // previous mex = x + 1
              dp1[x + 1] = add(dp1[x + 1], dp1[x + 1]);   // 0 1 2 3  +3
              dp2[x + 1] = add(dp2[x + 1], dp2[x + 1]);   // 0 1 2 4  +2
  
              // previous mex = x
              dp1[x + 1] = add(dp1[x + 1], dp1[x]);       // 0 1 2 3  +4
  
              // previous mex = x - 1
              if(x > 0) {
                  dp2[x - 1] = add(dp2[x - 1], dp2[x - 1]);  // 0 1 2 4 2  +4
                  dp2[x - 1] = add(dp2[x - 1], dp1[x - 1]);
              }
          }
  
          for(int i = 0; i <= n + 1; i++) {
              //ans = add(ans, add(dp1[i], dp2[i]));
              ans = add(ans, dp1[i]);
              ans = add(ans, dp2[i]);
          }
  
          Writer.println(ans);
      }
  
      private int add(int x, int y) {
          return (x + y) % MOD;
      }
  
      void solve() {
          for(int T = Reader.nextInt(); T > 0; T--) go();
      }
      void run() throws Exception {
          Reader.init(System.in);
          Writer.init(System.out);
          solve();
          Writer.close();
      }
  
      public static void main(String[] args) throws Exception {
          new D().run();
      }
  
      public static class Reader {
          public static StringTokenizer st;
          public static BufferedReader br;
  
          public static void init(InputStream in) {
              br = new BufferedReader(new InputStreamReader(in));
              st = new StringTokenizer("");
          }
  
          public static String next() {
              while(!st.hasMoreTokens()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }
              }
              return st.nextToken();
          }
  
          public static int nextInt() {
              return Integer.parseInt(next());
          }
  
          public static long nextLong() {
              return Long.parseLong(next());
          }
  
          public static double nextDouble() {
              return Double.parseDouble(next());
          }
      }
  
      public static class Writer {
          public static PrintWriter pw;
  
          public static void init(OutputStream os) {
              pw = new PrintWriter(new BufferedOutputStream(os));
          }
  
          public static void print(String s) {
              pw.print(s);
          }
  
          public static void print(int x) {
              pw.print(x);
          }
  
          public static void print(long x) {
              pw.print(x);
          }
  
          public static void println(String s) {
              pw.println(s);
          }
  
          public static void println(int x) {
              pw.println(x);
          }
  
          public static void println(long x) {
              pw.println(x);
          }
  
          public static void close() {
              pw.close();
          }
      }
  }