description: One day, early in the morning, you decided to buy yourself a bag of chips in the nearby store. The store has chips of n different flavors. A bag of the i-th flavor costs a_i burles.
  
  The store may run out of some flavors, so you'll decide which one to buy after arriving there. But there are two major flaws in this plan: 
  
    1. you have only coins of 1, 2 and 3 burles; 
    2. since it's morning, the store will ask you to pay in exact change, i. e. if you choose the i-th flavor, you'll have to pay exactly a_i burles. 
  
  
  
  Coins are heavy, so you'd like to take the least possible number of coins in total. That's why you are wondering: what is the minimum total number of coins you should take with you, so you can buy a bag of chips of any flavor in exact change?
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.
  
  The first line of each test case contains the single integer n (1 ≤ n ≤ 100) — the number of flavors in the store.
  
  The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the cost of one bag of each flavor.
  
  Output
  
  For each test case, print one integer — the minimum number of coins you need to buy one bag of any flavor you'll choose in exact change.
  
  Example
  
  Input
  
  
  4
  1
  1337
  3
  10 8 10
  5
  1 2 3 4 5
  3
  7 77 777
  
  
  Output
  
  
  446
  4
  3
  260
  
  Note
  
  In the first test case, you should, for example, take with you 445 coins of value 3 and 1 coin of value 2. So, 1337 = 445 ⋅ 3 + 1 ⋅ 2.
  
  In the second test case, you should, for example, take 2 coins of value 3 and 2 coins of value 2. So you can pay either exactly 8 = 2 ⋅ 3 + 1 ⋅ 2 or 10 = 2 ⋅ 3 + 2 ⋅ 2.
  
  In the third test case, it's enough to take 1 coin of value 3 and 2 coins of value 1.
solution: import java.io.*;
  import java.util.*;
  
  public class Main {
      class JoinSet {
          int[] fa;
          JoinSet(int n){
              fa = new int[n];
              for(int i = 0;i < n;i++) fa[i] = i;
          }
          int find(int x){
              if(x != fa[x]) fa[x] = find(fa[x]);
              return fa[x];
          }
          void join(int x, int y){
              x = find(x);
              y = find(y);
              fa[x] = y;
          }
      }
      static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
      static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
      static int mod = (int)1e9+7;
      static boolean[] isprime=new boolean[1];
      static {
          for(int i=2;i<isprime.length;i++) isprime[i]=true;
          for(int i=2;i<isprime.length;i++) {
              if(isprime[i]) {
                  for(int k = 2; i*k<isprime.length; k++) {
                      isprime[i*k] = false;
                  }
              }
          }
      }
      public static long gcd(long a, long b){
          return b == 0 ? a : gcd(b,a%b);
      }
      public static long lcm(long a, long b){
          return a*b / gcd(a,b);
      }
      public static int get() throws Exception{
          String ss = bf.readLine();
          if (ss.contains(" ")) ss = ss.substring(0, ss.indexOf(" "));
          return Integer.parseInt(ss);
      }
      public static int[] getInt() throws Exception {
          String s[] = bf.readLine().split(" ");
          int[] a = new int[s.length];
          for(int i = 0;i < a.length;i++){
              a[i] = Integer.parseInt(s[i]);
          }
          return a;
      }
      public static long[] getLong() throws Exception {
          String s[] = bf.readLine().split(" ");
          long[] a = new long[s.length];
          for(int i = 0;i < a.length;i++){
              a[i] = Long.parseLong(s[i]);
          }
          return a;
      }
      public static void print(int[] a) throws Exception {
          for(int i : a){
              bw.write(i + " ");
          }
          println();
      }
      public static void print(long[] a) throws Exception {
          for(long i : a){
              bw.write(i + " ");
          }
          println();
      }
      public static void println() throws Exception{
          bw.write("\n");
      }
      public static long pow(long a, long b){
          long ans = 1;
          while(b > 0){
              if((b&1) == 1){
                  ans *= a;
              }
              a*=a;
              b>>=1;
          }
          return ans;
      }
      public static int powmod(long a, long b, int mod){
          long ans = 1;
          while(b > 0){
              if((b&1) == 1){
                  ans = ans * a % mod;
              }
              a = a * a % mod;
              b>>=1;
          }
          return (int)ans;
      }
      public static void sort(int[] a){
          int n = a.length;
          Integer[] b = new Integer[n];
          for(int i = 0;i < n;i++) b[i] = a[i];
          Arrays.sort(b);
          for(int i = 0;i < n;i++) a[i] = b[i];
      }
  
      public static void main(String[] args) throws Exception {
          int t = get();
          while (t-- > 0){
              int n = get();
              int[] a = getInt();
              Set<Integer> set = new HashSet<>();
              int max = Arrays.stream(a).max().getAsInt();
              int ans = 0;
              boolean f1 = false, f2 = false;
              for(int i : a){
                  set.add(i);
                  if(i != max && i % 3 == 2) f2 = true;
                  if(i != max && i % 3 == 1) f1 = true;
              }
              if(max % 3 == 0){
                  ans = max/3;
                  if(f2 || f1)  ans++;
              }else if(max % 3 == 1){
                  ans = max/3+1;
                  if(f2 && (set.contains(max-1) || set.contains(1)))  ans++;
              }else{
                  ans = max/3+1;
                  if(f1)  ans++;
              }
              bw.write(ans+"\n");
          }
          bw.flush();
      }
  }
  