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 D {
      static FastReader in;
      static PrintWriter out;
  
      public static int arrange(int[] a, int a1, int a2) {
          int best = 0;
          for (int i = 0; i < a.length; i++) {
              int current = Integer.MAX_VALUE;
              if (a[i] % 3 == 0)
                  current = 2 + a[i] / 3;
              if (a[i] - a1 >= 0 && (a[i] - a1) % 3 == 0)
                  current = Math.min(current, 2 + (a[i] - a1) / 3);
              if (a[i] - a2 >= 0 && (a[i] - a2) % 3 == 0)
                  current = Math.min(current, 2 + (a[i] - a2) / 3);
              if (a[i] - a1 - a2 >= 0 && (a[i] - a1 - a2) % 3 == 0)
                  current = Math.min(current, 2 + (a[i] - a1 - a2) / 3);
              if (current == Integer.MAX_VALUE)
                  return -1;
              best = Math.max(best, current);
          }
          return best;
      }
  
      public static int arrange(int[] a, int a1) {
          int best = 0;
          for (int i = 0; i < a.length; i++) {
              int current = Integer.MAX_VALUE;
              if (a[i] % 3 == 0)
                  current = 1 + a[i] / 3;
              if (a[i] - a1 >= 0 && (a[i] - a1) % 3 == 0)
                  current = 1 + (a[i] - a1) / 3;
              best = Math.max(best, current);
          }
          return best;
      }
  
      public static int arrange(int[] a) {
          int best = 0;
          for (int i = 0; i < a.length; i++) {
              int current = Integer.MAX_VALUE;
              if (a[i] % 3 == 0)
                  current = a[i] / 3;
              best = Math.max(best, current);
          }
          return best;
      }
  
      public static void main(String[] args) {
          in = new FastReader();
          out = new PrintWriter(System.out);
  
          int t = in.nextInt();
          while(t-- > 0) {
              int n = in.nextInt();
              int[] a = new int[n];
              for (int i = 0; i < n; i++)
                  a[i] = in.nextInt();
  
              boolean mod1 = false, mod2 = false;
              for (int i = 0; i < n; i++) {
                  if (a[i] % 3 == 1)
                      mod1 = true;
                  if (a[i] % 3 == 2)
                      mod2 = true;
              }
  
              int answer = Integer.MAX_VALUE;
              if (mod1 && mod2) {
                  int current = arrange(a, 1, 2);
                  if (current != -1)
                      answer = Math.min(answer, current);
                  current = arrange(a, 2, 2);
                  if (current != -1)
                      answer = Math.min(answer, current);
              } else {
                  if (mod1) {
                      answer = arrange(a, 1);
                  }
                  if (mod2) {
                      answer = arrange(a, 2);
                  }
                  if (!mod1 && !mod2) {
                      answer = arrange(a);
                  }
              }
              out.println(answer);
          }
  
          out.flush();
          out.close();
      }
  
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          FastReader() {
              this(System.in);
          }
  
          FastReader(String file) throws FileNotFoundException {
              this(new FileInputStream(file));
          }
  
          FastReader(InputStream is) {
              br = new BufferedReader(new InputStreamReader(is));
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
  
          double nextDouble() {
              return Double.parseDouble(next());
          }
  
          String next() {
              while (st == null || !st.hasMoreTokens()) {
                  st = new StringTokenizer(nextLine());
              }
              return st.nextToken();
          }
  
          String nextLine() {
              String line;
              try {
                  line = br.readLine();
              } catch (IOException e) {
                  throw new RuntimeException(e);
              }
              return line;
          }
      }
  }
  