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 Edu119D{
	public static void main(String[] main) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		PrintWriter out = new PrintWriter(System.out);
		int t = Integer.parseInt(st.nextToken());
		for(int trial = 1; trial <= t; trial++){
			st = new StringTokenizer(br.readLine());
			int n = Integer.parseInt(st.nextToken());
			st = new StringTokenizer(br.readLine());
			int min = 1000000000;
			int max = 0;
			int second = 0;
			boolean rem0 = false;
			boolean rem1 = false;
			boolean rem2 = false;
			for(int i = 0; i < n; i++) {
				int m = Integer.parseInt(st.nextToken());
				min = Math.min(m, min);
				if (max > m)
					second = Math.max(m, second);
				else
					max = m;
				if(!rem0)
					rem0 = m%3 == 0;
				if(!rem1)
					rem1 = m%3 == 1;
				if(!rem2)
					rem2 = m%3 == 2;
			}
			if(max%3 == 0 && !rem1 && !rem2) 
				out.println(max / 3);
			else if(max%3 == 0)
				out.println(max / 3 + 1);
			else if(max%3 == 1 && (second == max-1 || min == 1) && rem2)
				out.println(max / 3 + 2);
			else if(max%3 == 1)
				out.println(max / 3 + 1);
			else if(max%3 == 2 && rem1)
				out.println(max / 3 + 2);
			else
				out.println(max / 3 + 1);
		}
		out.close();
	}
}