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.*;
import java.lang.Math;
public class Solution {
  static long MOD = 1000000007L;
  public static void print(long[] lwler){
  	for(int i=0;i<lwler.length;++i){
  			System.out.print(lwler[i]+" ");
  		}
  		System.out.println();
  }
  public static void print(int[] lwler){
  	for(int i=0;i<lwler.length;++i){
  			System.out.print(lwler[i]+" ");
  		}
  		System.out.println();
  }
  public static void main(String[] args) {
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
  	int tt = in.nextInt();
  	loop: for(int _m = 0; _m<tt; ++_m){
      int n = in.nextInt();
      int[] arr = new int[n];
      for(int i=0;i<n;++i){
        arr[i]=in.nextInt();
      }
      Arrays.sort(arr);
      int end = arr[n-1];
      boolean b = true;
      int res = 0;
      if(end==1){
        System.out.println("1");
        continue;
      }
      if(end%3==0){
        for(int ele : arr){
          if(ele%3!=0){
            b=false;
            break;
          }
        }
        res=b?end/3:(end/3+1);
      }
      else if(end%3==2){
        for(int ele : arr){
          if(ele%3==1){
            b=false;
            break;
          }
        }
        res=b?end/3:(end/3+1);
        ++res;
      }
      else{
        boolean b1 = true, b2 = true;
        for(int ele : arr){
          if(ele%3==2){
            b1=false;
            break;
          }
        }
        for(int ele : arr){
          if(ele==1||ele==end-1){
            b2=false;
            break;
          }
        }
        //System.out.println(b1+" "+b2);
        if(b1==false&&b2==false){
          b=false;
        }
        res=b?end/3:(end/3+1);
        ++res;
      }
      System.out.println(res);
    }
  }
}