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 D {
    static FastReader in;
    static PrintWriter out;

    public static int arrange(int[] a, int a1, int a2) {
        int best = 0;
        for (int i = 0; i < a.length; i++) {
            int current = Integer.MAX_VALUE;
            if (a[i] % 3 == 0)
                current = 2 + a[i] / 3;
            if ((a[i] - a1) % 3 == 0)
                current = Math.min(current, 2 + (a[i] - a1) / 3);
            if ((a[i] - a2) % 3 == 0)
                current = Math.min(current, 2 + (a[i] - a2) / 3);
            if ((a[i] - a1 - a2) % 3 == 0)
                current = Math.min(current, 2 + (a[i] - a1 - a2) / 3);
            if (current == Integer.MAX_VALUE)
                return -1;
            best = Math.max(best, current);
        }
        return best;
    }

    public static int arrange(int[] a, int a1) {
        int best = 0;
        for (int i = 0; i < a.length; i++) {
            int current = Integer.MAX_VALUE;
            if (a[i] % 3 == 0)
                current = 1 + a[i] / 3;
            if ((a[i] - a1) % 3 == 0)
                current = 1 + (a[i] - a1) / 3;
            best = Math.max(best, current);
        }
        return best;
    }

    public static int arrange(int[] a) {
        int best = 0;
        for (int i = 0; i < a.length; i++) {
            int current = Integer.MAX_VALUE;
            if (a[i] % 3 == 0)
                current = a[i] / 3;
            best = Math.max(best, current);
        }
        return best;
    }

    public static void main(String[] args) {
        in = new FastReader();
        out = new PrintWriter(System.out);

        int t = in.nextInt();
        while(t-- > 0) {
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextInt();

            boolean mod1 = false, mod2 = false;
            for (int i = 0; i < n; i++) {
                if (a[i] % 3 == 1)
                    mod1 = true;
                if (a[i] % 3 == 2)
                    mod2 = true;
            }

            int answer = Integer.MAX_VALUE;
            if (mod1 && mod2) {
                int current = arrange(a, 1, 2);
                if (current != -1)
                    answer = Math.min(answer, current);
                current = arrange(a, 2, 2);
                if (current != -1)
                    answer = Math.min(answer, current);
            } else {
                if (mod1) {
                    answer = arrange(a, 1);
                }
                if (mod2) {
                    answer = arrange(a, 2);
                }
                if (!mod1 && !mod2) {
                    answer = arrange(a);
                }
            }
            out.println(answer);
        }

        out.flush();
        out.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader() {
            this(System.in);
        }

        FastReader(String file) throws FileNotFoundException {
            this(new FileInputStream(file));
        }

        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

        String nextLine() {
            String line;
            try {
                line = br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
    }
}
