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.Arrays;
  
  public class D {
      public static void main(String[] args) throws IOException {
          FastScanner scanner = new FastScanner();
          int t = scanner.nextInt();
          while (t-- > 0) {
              int n = scanner.nextInt();
              int[] a = new int[n];
              int max = Integer.MIN_VALUE;
              boolean remainder1 = false, remainder2 = false, hasOne = false;
              for (int i = 0; i < n; i++) {
                  a[i] = scanner.nextInt();
                  if (a[i] % 3 == 1) remainder1 = true;
                  else if (a[i] % 3 == 2) remainder2 = true;
                  if (a[i] == 1) hasOne = true;
                  max = Math.max(max, a[i]);
              }
  
  
              if (max % 3 == 0) {
                  if (remainder1 || remainder2) {
                      System.out.println(max / 3 + 1);
                  } else {
                      System.out.println(max / 3);
                  }
              } else if (max % 3 == 1) {
                  if (!remainder2) {
                      System.out.println(max / 3 + 1);
                  } else {
                      boolean hasMaxMinusOne = false;
                      for (int i : a)
                          if (i == max - 1) { hasMaxMinusOne = true; break; }
                      System.out.println(max / 3 + (hasMaxMinusOne || hasOne ? 2 : 1));
                  }
              } else {  // max % 3 == 2
                  if (remainder1) {
                      System.out.println(max / 3 + 2);
                  } else {
                      System.out.println(max / 3 + 1);
                  }
              }
          }
      }
  
      /**
       * Credits: https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
       */
      private static class FastScanner implements Closeable {
          final private int BUFFER_SIZE = 1 << 16;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
  
          public FastScanner() {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public FastScanner(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[64];
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n' || c == '\r') {
                      if (cnt != 0) {
                          break;
                      } else {
                          continue;
                      }
                  }
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          public String next() throws IOException {
              return next(32);
          }
  
          public String next(int len) throws IOException {
              byte[] buf = new byte[len];
              int ptr = 0;
              byte c = read();
              while (c <= ' ') c = read();
              do {
                  if (ptr == buf.length) {
                      buf = Arrays.copyOf(buf, buf.length << 1);
                  }
                  buf[ptr++] = c;
              } while ((c = read()) > ' ');
              if (buf.length == ptr) return new String(buf);
              return new String(Arrays.copyOf(buf, ptr));
          }
  
          public int nextInt() throws IOException {
              int ret = 0;
              byte c = read();
              while (c <= ' ') c = read();
              boolean neg = (c == '-');
              if (neg) c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (neg) return -ret;
              return ret;
          }
  
          public long nextLong() throws IOException {
              long ret = 0;
              byte c = read();
              while (c <= ' ') c = read();
              boolean neg = (c == '-');
              if (neg) c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (neg) return -ret;
              return ret;
          }
  
          public double nextDouble() throws IOException {
              double ret = 0, div = 1;
              byte c = read();
              while (c <= ' ') c = read();
              boolean neg = (c == '-');
              if (neg) c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (c == '.') {
                  while ((c = read()) >= '0' && c <= '9') {
                      ret += (c - '0') / (div *= 10);
                  }
              }
              if (neg) return -ret;
              return ret;
          }
  
          private void fillBuffer() throws IOException {
              bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
              if (bytesRead == -1) buffer[0] = -1;
          }
  
          private byte read() throws IOException {
              if (bufferPointer == bytesRead) fillBuffer();
              return buffer[bufferPointer++];
          }
  
          @Override
          public void close() throws IOException {
              if (din == null) return;
              din.close();
          }
      }
  }
  