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 {
    public static void main(String[] args) {
        while (N-- > 0) {
            solve();
        }
        out.close();
    }

    public static void solve() {
        int M = sc.nextInt();
        int[] a = sc.readArray(M);
        boolean e1 = false;
        boolean e2 = false;
        boolean e3 = false;
        boolean c1 = false;

        int max = 0;

        for (int i = 0; i < M; i++) {
            if (!e1 && a[i] % 3 == 1) {
                e1 = true;
            } else if (!e2 && a[i] % 3 == 2) {
                e2 = true;
            } else if (!e3 && a[i] % 3 == 0) {
                e3 = true;
            }
            if (!c1 && a[i] == 1) {
                c1 = true;
            }
            max = Math.max(max, a[i]);
        }

        if (max % 3 == 0) {
            if (e1 || e2) {
                out.println(max / 3 + 1);
            } else {
                out.println(max / 3);
            }
        }

        if (max % 3 == 1) {
            if (c1) {
                for (int i = 0; i < M; i++) {
                    if (a[i] == max - 1) {
                        out.println(max / 3 + 2);
                        return;
                    }
                }
            } else {
                out.println(max / 3 + 1);
            }
        }

        if (max % 3 == 2) {
            if (e1) {
                out.println(max / 3 + 2);
            } else {
                out.println(max / 3 + 1);
            }
        }
    }

    private static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    private static MyScanner sc = new MyScanner();

    private static int N = sc.nextInt();

    @SuppressWarnings("unused")
    private static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                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());
        }

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

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}