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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class D1620 {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        for (int i = 0; i < t; i++) {
            int n = Integer.parseInt(br.readLine());
            int[] ar = new int[n];
            StringTokenizer st = new StringTokenizer(br.readLine());
            for (int j = 0; j < n; j++) ar[j] = Integer.parseInt(st.nextToken());
            int ans = Integer.MAX_VALUE;
            for (int j = 0; j < 3; j++) {
                 for (int k = 0; k < 3; k++) {
                    //j = # of 1; k = # of 2
                    int[][] mod3 = new int[10][2];
                    mod3[0][0] = 1;
                    mod3[0][1] = 0;
                    for (int l = 0; l < 10; l++) mod3[l][1] = Integer.MAX_VALUE;
                    for (int l = 0; l <= j; l++) {
                        for (int m = 0; m <= k; m++) {
                            mod3[l + m * 2][0] = 1;
                            mod3[l + m * 2][1] = Math.min(l + m,  mod3[l + m * 2][1]);
                        }
                    }
                    int mx = 0;
                    for (int l = 0; l < n; l++) {
                        int mod = ar[l] % 3;
                        int mn = Integer.MAX_VALUE;
                        while (mod <= ar[l] && mod <= 9){
                            if(mod3[mod][0] == 1) {
                                mn = Math.min((ar[l] - mod)/3, mn);
                            }
                            mod += 3;
                        }
                        mx = Math.max(mx, mn);
                    }
                    if(mx == Integer.MAX_VALUE) continue;
                    ans = Math.min(ans, mx + j + k);
                }
            }
            System.out.println(ans);
        }
    }
}
