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

    /**
     * D_Exact_Change
     */

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

    public class D_Exact_Change {
    

        static class FastReader {
            BufferedReader br;
            StringTokenizer st;
     
            public FastReader()
            {
                br = new BufferedReader(
                    new InputStreamReader(System.in));
            }
     
            String next()
            {
                while (st == null || !st.hasMoreElements()) {
                    try {
                        st = new StringTokenizer(br.readLine());
                    }
                    catch (IOException e) {
                        e.printStackTrace();
                    }
                }
                return st.nextToken();
            }
     
            int nextInt() { return Integer.parseInt(next()); }
     
            long nextLong() { return Long.parseLong(next()); }
     
            double nextDouble()
            {
                return Double.parseDouble(next());
            }
     
            String nextLine()
            {
                String str = "";
                try {
                    str = br.readLine();
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
                return str;
            }
        }

        public static void main(String[] args) {
            FastReader fr = new FastReader();
            int t = fr.nextInt();
            while(t-->0) {
                int n = fr.nextInt();
                long[] arr = new long[n];



                long maxN = Integer.MIN_VALUE;

                for(int i = 0;i<n;++i)
                {
                arr[i] = fr.nextLong();
                maxN = Math.max(maxN, arr[i]);
                }

                long max = (long)Math.ceil(maxN/3.0);
                long ans = Integer.MAX_VALUE;

                for(long ones= 0;ones<=2;++ones)
                {
                    for(long twos = 0;twos<=2;++twos)
                    {
                        for(long threes = max-4 ;threes<=max;++threes)
                        {
                            long coins = ones+twos+threes;

                            boolean ok = true;

                            for(int i = 0;i<n;++i)
                            {
                                boolean found = false;

                                for(int o = 0;o<=ones;++o)
                                {
                                    for(int tw = 0;tw<=twos;++tw)
                                    {
                                        long rem = arr[i] - o - (2*tw);

                                        if((rem>=0 && rem%3==0 && rem/3<=threes)) found = true;
                                    }
                                }

                                if(!found) ok = false;

                            }

                            if(ok) ans = Math.min(coins,ans);
                        }
                    }
                }

                System.out.println(ans);
            }
        }
    }