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 ExactChange {
    public static void main(String[] args) throws IOException {
        Reader in = new Reader();
        PrintWriter out = new PrintWriter(System.out);
        
        int T = in.nextInt();
        for (int t = 0; t < T; t++) {
            int N = in.nextInt();
            int[] arr = new int[N];
            for (int i = 0; i < N; i++) {
                arr[i] = in.nextInt();
            }
            int res = Integer.MAX_VALUE;
            for (int one = 0; one <= 2; one++) {
                t: for (int two = 0; two <= 2; two++) {
                    int three = 0;
                    for (int i : arr) {
                        int min = Integer.MAX_VALUE;
                        for (int x = 0; x <= one; x++) {
                            for (int y = 0; y <= two; y++) {
                                int n = i - x - y * 2;
                                if (n >= 0 && n % 3 == 0) {
                                    min = Math.min(min, n / 3);
                                }
                            }
                        }
                        if (min == Integer.MAX_VALUE) {
                            continue t;
                        }
                        three = Math.max(three, min);
                    }
                    res = Math.min(res, one + two + three);
                }
            }
            out.println(res);
        }
        
        out.close();
    }
    static class Reader {
        BufferedReader in;
        StringTokenizer st;
        public Reader() {
            in = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer("");
        }
        public String nextLine() throws IOException {
            st = new StringTokenizer("");
            return in.readLine();
        }
        public String next() throws IOException {
            while (!st.hasMoreTokens()) {
                st = new StringTokenizer(in.readLine());
            }
            return st.nextToken();
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
    public static void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int i : arr) {
            list.add(i);
        }
        Collections.sort(list);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = list.get(i);
        }
    }
}