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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.StringTokenizer;

public class A4 {

    void solve() {
        int n = cint();
        int[] a = carr_int(n);
        Arrays.sort(a);

        int res = a[n-1];
        int till3 = a[n-1] / 3 + 3;
        int from3 = Math.max(0, a[n-1] / 3 - 3);
        for (int x1 = 0; x1 <= 2; x1++) {
            for (int x2 = 0; x2 <= 2; x2++) {
                for (int x3 = from3; x3 <= till3; x3++) {
                    
                    if (x1 + x2 + x3 >= res) {
                        continue;
                    }
                    
                    boolean ok = true;
                    for (int i = 0; i < n; i++) {
                        if (!can(a[i], x1, x2, x3)) {
                            ok = false;
                            break;
                        }
                    }
                    
                    if (ok) {
                        res = x1 + x2 + x3;
                    }
                }
            }
        }
        
        cout(res);
    }

    boolean can(int a, int x1, int x2, int x3) {
        for (int c1 = 0; c1 <= x1; c1++) {
            for (int c2 = 0; c2 <= x2; c2++) {
                int y = a - c1 - c2 * 2;
                if (y % 3 == 0 && y / 3 <= x3) {
                    return true;
                }
            }
        }
        return false;
    }
    

    public static void main(String... args) {
        int t = in.nextInt();
        for (int test = 0; test < t; test++) {
            new A4().solve();
        }
        out.flush();
    }

    static final QuickReader in = new QuickReader(System.in);
    static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out, 131_072));

    static int cint() {
        return in.nextInt();
    }

    static long clong() {
        return in.nextLong();
    }

    static String cstr() {
        return in.nextLine();
    }

    static int[] carr_int(int n) {
        return in.nextInts(n);
    }

    static long[] carr_long(int n) {
        return in.nextLongs(n);
    }

    static void cout(int... a) {
        StringBuilder buf = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            if (i != 0) {
                buf.append(' ');
            }
            buf.append(a[i]);
        }
        out.println(buf);
    }

    static void cout(long... a) {
        StringBuilder buf = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            if (i != 0) {
                buf.append(' ');
            }
            buf.append(a[i]);
        }
        out.println(buf);
    }

    static void cout(Object o) {
        out.println(o);
    }

    static class QuickReader {
        BufferedReader in;
        StringTokenizer token;

        public QuickReader(InputStream ins) {
            in = new BufferedReader(new InputStreamReader(ins));
            token = new StringTokenizer("");
        }

        public boolean hasNext() {
            while (!token.hasMoreTokens()) {
                try {
                    String s = in.readLine();
                    if (s == null) {
                        return false;
                    }
                    token = new StringTokenizer(s);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return true;
        }

        public String next() {
            hasNext();
            return token.nextToken();
        }

        public String nextLine() {
            try {
                String s = in.readLine();
                token = new StringTokenizer("");
                return s;
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }

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

        public int[] nextInts(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

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

        public long[] nextLongs(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }
    }
}
