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.PrintStream;
  import java.util.*;
  
  public class D {
  
      static int[][] d = new int[1000002][2];
      static final int MOD = 998244353;
  
      public static void main(String[] args) {
          Scanner sc = new Scanner(System.in);
          PrintStream out = System.out;
  
          int t = sc.nextInt();
  
          for (int i = 0; i < t; i++) {
              int n = sc.nextInt();
              int[] arr = new int[n];
              for (int j = 0; j < n; j++) {
                  arr[j] = sc.nextInt();
              }
              out.println(solve(arr));
          }
  
      }
  
      private static int solve(int[] arr) {
          int res = 0;
          Set<Integer> nonzero = new TreeSet<>();
          int oneCount = 0;
          for (int a : arr) {
              if (a == 1) {
                  oneCount++;
              }
              int deltaPlusNo = (d[a][0] + d[a + 1][0]) % MOD;
              int deltaPlusYes = d[a + 1][1];
              int deltaMinusYes = (a > 0 ? d[a - 1][0] + d[a - 1][1] : 0) % MOD;
              d[a + 1][0] = (d[a + 1][0] + deltaPlusNo) % MOD;
              d[a + 1][1] = (d[a + 1][1] + deltaPlusYes) % MOD;
              nonzero.add(a + 1);
              if (a == 0) {
                  d[1][0] = (d[1][0] + 1) % MOD;
                  nonzero.add(1);
              } else {
                  d[a - 1][1] = (d[a - 1][1] + deltaMinusYes) % MOD;
                  nonzero.add(a - 1);
              }
          }
          for (int index : nonzero) {
              res = (res + d[index][0]) % MOD;
              res = (res + d[index][1]) % MOD;
              d[index][0] = 0;
              d[index][1] = 0;
          }
          int pow = 1;
          for (int i = 0; i < oneCount; i++) {
              pow = (pow * 2) % MOD;
          }
          res = (res + pow - 1) % MOD;
          return res;
      }
  }
  