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 _1620_D {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int t = Integer.parseInt(in.readLine());
        while(t-- > 0) {
            int n = Integer.parseInt(in.readLine());
            StringTokenizer line = new StringTokenizer(in.readLine());
            int[] a = new int[n];
            int max = 0;
            for(int i = 0; i < n; i++) {
                a[i] = Integer.parseInt(line.nextToken());
                max = Math.max(max, a[i]);
            }
            int min = Integer.MAX_VALUE;
            int threes = max / 3;
            for(int i = threes - 1; i <= threes; i++) {
                for(int j = 0; j <= 2; j++) {
                    for(int k = 0; k <= 2; k++) {
                        if(valid(i, j, k, a)) {
                            min = Math.min(min, i + j + k);
                        }
                    }
                }
            }
            out.println(min);
        }
        in.close();
        out.close();
    }
    static boolean valid(int threes, int twos, int ones, int[] a) {
        for(int i = 0; i < a.length; i++) {
            if(threes >= a[i] / 3) {
                int left = a[i] % 3;
                if(left == 1) {
                    if(ones == 0 && (twos < 2 || a[i] == 1)) {
                        return false;
                    }
                }else if(left == 2) {
                    if(twos == 0 && ones < 2) {
                        return false;
                    }
                }
            }else {
                if(threes * 3 + twos * 2 + ones < a[i]) {
                    return false;
                }
                int left = a[i] - threes * 3;
                if(left % 2 == 1 && ones == 0) {
                    return false;
                }
            }
        }
        return true;
    }
}
