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.
1
1
6006

2002

import java.util.*;
import java.io.*;

public class Template  {
	// remember long, to reformat ctrl + shift +f
	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
    public static boolean can(int o,int t, int three,int a) {
    	a-=Math.min(a/3, three)*3;
    	a-=Math.min((a/2)*2, 2*t);
    	a-=Math.min(a, o);
    	return a==0;
    	
    }
	  
 
	public static void main(String[] args) throws Exception {
     int t=sc.nextInt();
     while(t-->0) {
          
      int n=sc.nextInt();
      int max3=0;
      int one =0;
      int two=0;
      int arr[]=new int[n];
      for(int i=0;i<n;i++) {
    	  int a=sc.nextInt();
    	  int three=a/3;
    	  max3=Math.max(max3, three);
    	  arr[i]=a;
    	   
    	  
      }
      int max=Integer.MAX_VALUE;
      for(int threes =Math.max(max3-2,0);threes<=max3;threes++) {
    	  for(int twos = 0;twos<=3;twos++)
    		  for(int ones = 0;ones<3;ones++) {
    			  boolean possible = true;
    			  for(int i=0;i<n;i++) {
    				  if(!can(ones,twos,threes,arr[i])) {
    					  possible =false;
    					  break;
    				  }
    			  }
    			  if(possible)
    				  max =Math.min(max, ones+twos+threes);
    		  }
    	  
      }
      pw.println(max);
  
      

    	 
     }
		
		
	 pw.close();

	}

	// --------------------stuff ----------------------
	static class pair implements Comparable<pair> {
		int v;
		int w;
        
		public pair(int v,int  w) {
			this.v = v;
			this.w = w;
			
		}

		public int compareTo(pair p) {
			return this.w- p.w;// increasing order!!
		
			//return Double.compare(v*w, p.w*p.v);
		
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public long[] nextlongArray(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public Long[] nextLongArray(int n) throws IOException {
			Long[] a = new Long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] a = new Integer[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}

}