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 static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;

public class Problem_D {
	private final static int INF = (int) 1e9 + 5;
	
	public static void main(String[] dummy) {
		MyScanner ms = new MyScanner();
		PrintStream out = new PrintStream(System.out);
		
		int testcases = ms.nextInt();
		while (testcases-- > 0) {
			int N = ms.nextInt();
			int []A = ms.readArray(N);
			int min_coin = INF;
			
			for (int ones = 0; ones <= 1; ones++) {
				for (int twos = 0; ones + twos <= 2; twos++) {
					int threes = 0;
					
					for (int a : A) {
						int max_three = INF;
						
						for (int i = 0; i <= ones; i++) {
							for (int j = 0; j <= twos; j++) {
								int x = a - i - (2 * j);
								
								if (x >= 0 && x % 3 == 0) 
									max_three = min(max_three, x / 3);
							}
						}
						threes = max(threes, max_three);
					}
					min_coin = min(min_coin, ones + twos + threes);
				}
			}
			out.println(min_coin);
		}
		
		double time = System.currentTimeMillis();
		out.println("\nExecution time: " + time + "s");
		out.flush();
		out.close();
	}
	
	public static void Sort(int[] arr) { // TODO : Collections.sort always uses Merge sort
		ArrayList<Integer> sorted = new ArrayList<>();
		for (int x : arr) 
			sorted.add(x);
		
		Collections.sort(sorted);
		for (int i = 0; i < arr.length; i++)
			arr[i] = sorted.get(i);
	}
	
	static class MyScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		
		String next() {
			while (!st.hasMoreTokens()) 
				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());
		}
		
		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) 
				a[i] = nextInt();
			return a;
		}
	}
}
