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.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.ArrayList;
  import java.util.Collections;
  import java.util.HashSet;
  import java.util.StringTokenizer;
  /*
  
  
  3
  2 3 4
  3
  
  3
  29 31 30
  
   */
  public class D {
  
  	public static void main(String[] args) {
  		FastScanner fs=new FastScanner();
  		int T=fs.nextInt();
  		for (int tt=0; tt<T; tt++) {
  			boolean[] valuesMod3=new boolean[3];
  //			boolean hit2=false, hit4=false, hitNon24=false;
  			boolean have1=false;
  			int max=0;
  			int n=fs.nextInt();
  			HashSet<Integer> values=new HashSet<>();
  			for (int i=0; i<n; i++) {
  				int x=fs.nextInt();
  				max=Math.max(max, x);
  				values.add(x);
  				valuesMod3[x%3]=true;
  				if (x==1) have1=true;
  			}
  			//everything %3 == 0, easy
  			if (!valuesMod3[1] && !valuesMod3[2]) {
  				System.out.println(max/3);
  				continue;
  			}
  			//only 0s and one other value
  			if (!valuesMod3[1] || !valuesMod3[2]) { //maybe?
  				System.out.println(max/3+1);
  				continue;
  			}
  			
  			//have at least a 1 and a 2, %3
  			if (have1) {
  				System.out.println((max+2)/3+1);	
  				continue;
  			}
  			else {
  				//this is the 2 3 4 case => 2, 2, 3
  //				if (valuesMod3[0] && valuesMod3[1] && valuesMod3[2] && max==4) {
  //					System.out.println(3);
  //					continue;
  //				}
  				if (max%3==1 && values.contains(max-1)) {
  					System.out.println((max+1)/3+1+1);
  					continue;
  				}
  			}
  			//take 2 2s, and all 3s
  			System.out.println((max+1)/3+1);
  		}
  	}
  
  	static void sort(int[] a) {
  		ArrayList<Integer> l=new ArrayList<>();
  		for (int i:a) l.add(i);
  		Collections.sort(l);
  		for (int i=0; i<a.length; i++) a[i]=l.get(i);
  	}
  	
  	static class FastScanner {
  		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
  		StringTokenizer st=new StringTokenizer("");
  		String next() {
  			while (!st.hasMoreTokens())
  				try {
  					st=new StringTokenizer(br.readLine());
  				} catch (IOException e) {
  					e.printStackTrace();
  				}
  			return st.nextToken();
  		}
  		
  		int nextInt() {
  			return Integer.parseInt(next());
  		}
  		int[] readArray(int n) {
  			int[] a=new int[n];
  			for (int i=0; i<n; i++) a[i]=nextInt();
  			return a;
  		}
  		long nextLong() {
  			return Long.parseLong(next());
  		}
  	}
  
  	
  }
  