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 Solution {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() {
            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());
        }
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    static void sort(int a[]){ // int -> long
        ArrayList<Integer> arr=new ArrayList<>(); // Integer -> Long
        for(int i=0;i<a.length;i++)
        arr.add(a[i]);
        Collections.sort(arr);
        for(int i=0;i<a.length;i++)
        a[i]=arr.get(i);
        
    }
    private static long gcd(long a, long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
    private static long pow(long x,long y){
        if(y==0)return 1;
        long temp = pow(x, y/2);
        if(y%2==1){
            return x*temp*temp;
        }
        else{
            return temp*temp;
        }
    }
    static int log(long n){
        int res = 0;
        while(n>0){
            res++;
            n/=2;
        }
        return res;
    }

    static int mod = (int)1e9+7;
    static PrintWriter out;
    static FastReader sc ;
    public static void main(String[] args) throws IOException {
        sc = new FastReader();
        out = new PrintWriter(System.out);
        // primes();
        // ================================ //
        int test = sc.nextInt();
        while (test-- > 0) {
            int n = sc.nextInt();
            int[]arr = new int[n];
            for(int i=0;i<n;i++)arr[i] = sc.nextInt();
            solver(arr, n);
        }
        // ================================ //
        // int n = sc.nextInt();
        // solver();
        // ================================ //
        out.flush();
    }

    public static void solver(int[]arr, int n) {
        // 0 0 
        long cur = 0;
        int max = 0;
        boolean one = false;
        boolean two = false;
        for(int i=0;i<n;i++){
            if(arr[i]%3==1){
                one=true;
            }
            if(arr[i]%3==2){
                two=true;
            }
            max = Math.max(arr[i], max);
        }

        cur = max/3;
        if(one && two && max%3==2)cur+=2;
        else if(one || two)cur++;

        out.println( cur);
    }
}
