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.*;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException {
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("cowjump.out")));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int t = Integer.parseInt(f.readLine());
        while(t-- > 0) {
            int n = Integer.parseInt(f.readLine());
            StringTokenizer st = new StringTokenizer(f.readLine());
            int[] a = new int[n];
            boolean[] mod = new boolean[3];
            for(int i = 0; i < n; i++) {
                a[i] = Integer.parseInt(st.nextToken());
                mod[a[i]%3] = true;
            }
            Arrays.sort(a);
            boolean flag = false;
            for(int i: a) {
                if(i == a[n-1]-1) {
                    flag = true;
                    break;
                }
            }
            if(!mod[1] && !mod[2]) {
                out.println(a[n-1]/3);
            } else if(!mod[1] || !mod[2]) {
                out.println(a[n-1]/3+1);
            } else if(a[0] == 1 || (a[n-1]%3 == 1 && flag)) {
                out.println((a[n-1]+2)/3+1);
            } else {
                out.println((a[n-1]+1)/3+1);
            }
        }
        f.close();
        out.close();
    }
}
