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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class D {
    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 sc = new FastReader();
        int t = sc.nextInt();
        StringBuilder s = new StringBuilder();
        while (t-->0){
            int n = sc.nextInt();
            int[] mod3 = new int[n];
            int[] p = new int[n];
            boolean has1 = false;
            boolean has2 = false;
            boolean has_1 =false;
            int maxp = Integer.MIN_VALUE;
            for (int i=0;i<n;i++){
                p[i] = sc.nextInt();
                mod3[i] = p[i]%3;
                if (mod3[i]==1){
                    has1 = true;
                }
                if (mod3[i]==2){
                    has2 = true;
                }
                if (p[i]==1){
                has_1 = true;
            }
                maxp = Math.max(maxp,p[i]);
            }

            int mod3_M = maxp%3;
            int min_count = maxp/3;


            if (mod3_M!=0){
                min_count ++;
                if (mod3_M==1&&has2){
                    boolean flag = false;
                    for (int i=0;i<n;i++){
                        if (p[i]==maxp-1){
                            flag = true;
                        }
                    }
                    if (has_1||flag){
                        min_count++;
                    }
                }else if (mod3_M==2&&has1){
                    min_count++;
                }
            }
            if (mod3_M==0){
                if (has1||has2){
                    min_count++;
                }
            }
            s.append(min_count+"\n");
        }
        System.out.println(s);
    }
}
