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.InputStreamReader;
  import java.util.StringTokenizer;
  import java.util.*;
  import java.io.*;
  public class Main {
      // Graph
      // prefix sums
      //inputs
      public static void main(String args[])throws Exception{
          Input sc=new Input();
          precalculates p=new precalculates();
          StringBuilder sb=new StringBuilder();
  
          int t=sc.readInt();
          for(int f=0;f<t;f++){
              int n=sc.readInt();
              int a[]=sc.readArray();
              int fu=n+2;
              long dp1[]=new long[fu];
              long dp2[]=new long[fu];
              long mod=998244353;
              long sum=0;
              dp1[0]=1;
              for(int i=0;i<n;i++){
                  if(a[i]>0){
                      dp2[a[i]-1]=(dp1[a[i]-1] + 2*dp2[a[i]-1])%mod;
                  }
                  dp1[a[i]+1]=(dp1[a[i]]+2*dp1[a[i]+1])%mod;
                  dp2[a[i]+1]=(2*dp2[a[i]+1])%mod;
              }
              for(int i=0;i<fu;i++){
                  sum+=dp1[i]+dp2[i];
                  sum%=mod;
              }
              sb.append((sum-1+mod)%mod+"\n");
  
          }
          System.out.print(sb);
      }
  }
  class Input{
      BufferedReader br;
      StringTokenizer st;
      Input(){
          br=new BufferedReader(new InputStreamReader(System.in));
          st=new StringTokenizer("");
      }
      public int[] readArray() throws Exception{
          st=new StringTokenizer(br.readLine());
          int a[]=new int[st.countTokens()];
          for(int i=0;i<a.length;i++){
              a[i]=Integer.parseInt(st.nextToken());
          }
          return a;
      }
      public long[] readArrayLong() throws Exception{
          st=new StringTokenizer(br.readLine());
          long a[]=new long[st.countTokens()];
          for(int i=0;i<a.length;i++){
              a[i]=Long.parseLong(st.nextToken());
          }
          return a;
      }
      public int readInt() throws Exception{
          st=new StringTokenizer(br.readLine());
          return Integer.parseInt(st.nextToken());
      }
      public long readLong() throws Exception{
          st=new StringTokenizer(br.readLine());
          return Long.parseLong(st.nextToken());
      }
      public String readString() throws Exception{
          return br.readLine();
      }
      public int[][] read2dArray(int n,int m)throws Exception{
          int a[][]=new int[n][m];
          for(int i=0;i<n;i++){
              st=new StringTokenizer(br.readLine());
              for(int j=0;j<m;j++){
                  a[i][j]=Integer.parseInt(st.nextToken());
              }
          }
          return a;
      }
  }
  class precalculates{
      public int[] prefixSumOneDimentional(int a[]){
          int n=a.length;
          int dp[]=new int[n];
          for(int i=0;i<n;i++){
              if(i==0)
                  dp[i]=a[i];
              else
                  dp[i]=dp[i-1]+a[i];
          }
          return dp;
      }
      public int[] postSumOneDimentional(int a[]) {
          int n = a.length;
          int dp[] = new int[n];
          for (int i = n - 1; i >= 0; i--) {
              if (i == n - 1)
                  dp[i] = a[i];
              else
                  dp[i] = dp[i + 1] + a[i];
          }
          return dp;
      }
      public int[][] prefixSum2d(int a[][]){
          int n=a.length;int m=a[0].length;
          int dp[][]=new int[n+1][m+1];
          for(int i=1;i<=n;i++){
              for(int j=1;j<=m;j++){
                  dp[i][j]=a[i-1][j-1]+dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1];
              }
          }
          return dp;
      }
      public long pow(long a,long b){
          long mod=1000000007;
          long ans=0;
          if(b<=0)
              return 1;
          if(b%2==0){
              ans=pow(a,b/2)%mod;
              return ((ans%mod)*(ans%mod))%mod;
          }else{
              return ((a%mod)*(ans%mod))%mod;
          }
      }
  
  }
  class GraphInteger{
      HashMap<Integer,vertex> vtces;
      class vertex{
          HashMap<Integer,Integer> children;
          public vertex(){
              children=new HashMap<>();
          }
      }
      public GraphInteger(){
          vtces=new HashMap<>();
      }
      public void addVertex(int a){
          vtces.put(a,new vertex());
      }
      public void addEdge(int a,int b,int cost){
          if(!vtces.containsKey(a)){
              vtces.put(a,new vertex());
          }
          if(!vtces.containsKey(b)){
              vtces.put(b,new vertex());
          }
          vtces.get(a).children.put(b,cost);
  //        vtces.get(b).children.put(a,cost);
      }
      public boolean isCyclicDirected(){
          boolean isdone[]=new boolean[vtces.size()+1];
          boolean check[]=new boolean[vtces.size()+1];
          for(int i=1;i<=vtces.size();i++) {
              if (!isdone[i] && isCyclicDirected(i,isdone, check)) {
                  return true;
              }
          }
          return false;
      }
      private boolean isCyclicDirected(int i,boolean isdone[],boolean check[]){
          if(check[i])
              return true;
          if(isdone[i])
              return false;
          check[i]=true;
          isdone[i]=true;
          Set<Integer> set=vtces.get(i).children.keySet();
          for(Integer ii:set){
              if(isCyclicDirected(ii,isdone,check))
                  return true;
          }
          check[i]=false;
          return false;
      }
  }
  
  
  
  
  