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.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.List;

public class Main {

    static class Data {
        char type;
        int count;

        public Data(char type, int count) {
            this.type = type;
            this.count = count;
        }
    }

    public static void main(String[] args) throws Exception {
        int tc = io.nextInt();
        for (int i = 0; i < tc; i++) {
            solve();
        }
        io.close();
    }

    private static void solve() throws Exception {
        int n = io.nextInt();
        List<Integer> data = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            data.add(io.nextInt());
        }
        int max = Collections.max(data);
        int output = Integer.MAX_VALUE;
        for (int c1 = 0; c1 <= 3; c1++) {
            for (int c2 = 0; c2 <= 3; c2++) {
                int c3 = (int) Math.ceil((max - c1 - 2 * c2) / 3.0);
                c3 = Math.max(c3, 0);
                if (possible(data, c1, c2, c3)) {
                    output = Math.min(output, c1 + c2 + c3);
                }
            }
        }
        io.println(output);
    }

    private static boolean possible(List<Integer> data, int c1, int c2, int c3) {
        for (int d : data) {
            if (!possible(d, c1, c2, c3)) {
                return false;
            }
        }
        return true;
    }

    private static boolean possible(int d, int c1, int c2, int c3) {
        for (int i = 0; i <= c1; i++) {
            for (int j = 0; j <= c2; j++) {
                if (i + 2 * j > d) {
                    continue;
                }
                if ((d - i - 2 * j) % 3 != 0) {
                    continue;
                }
                if ((d - i - 2 * j) / 3 <= c3) {
                    return true;
                }
            }
        }
        return false;
    }


    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>(a.length);
        for (int i : a) {
            l.add(i);
        }
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

    //-----------PrintWriter for faster output---------------------------------
    public static FastIO io = new FastIO();

    //-----------MyScanner class for faster input----------
    static class FastIO extends PrintWriter {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar, numChars;

        // standard input
        public FastIO() {
            this(System.in, System.out);
        }

        public FastIO(InputStream i, OutputStream o) {
            super(o);
            stream = i;
        }

        // file input
        public FastIO(String i, String o) throws IOException {
            super(new FileWriter(o));
            stream = new FileInputStream(i);
        }

        // throws InputMismatchException() if previously detected end of file
        private int nextByte() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars == -1) {
                    return -1; // end of file
                }
            }
            return buf[curChar++];
        }

        // to read in entire lines, replace c <= ' '
        // with a function that checks whether c is a line break
        public String next() {
            int c;
            do {
                c = nextByte();
            } while (c <= ' ');
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = nextByte();
            } while (c > ' ');
            return res.toString();
        }

        public String nextLine() {
            int c;
            do {
                c = nextByte();
            } while (c < '\n');
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = nextByte();
            } while (c > '\n');
            return res.toString();
        }

        public int nextInt() {
            int c;
            do {
                c = nextByte();
            } while (c <= ' ');
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = nextByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = 10 * res + c - '0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }

        public long nextLong() {
            int c;
            do {
                c = nextByte();
            } while (c <= ' ');
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = nextByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = 10 * res + c - '0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }


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