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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;
import java.util.stream.Stream;

public class Program {

    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

    public static void main(String[] args) throws NumberFormatException, IOException {

        int cases = Integer.parseInt(reader.readLine());
//        int cases = 1;
        int mod = 998244353;

        while(cases-- > 0) {

            String[] firstLine = reader.readLine().split(" ");

            int n = Integer.parseInt(firstLine[0]);
            int[] arr = convertToIntPrimitiveArray();

            int total = Integer.MAX_VALUE;

            for(int j=0;j<=2;j++) {
                for(int k=0;k<=2;k++) {

                    int coins = 0;
                    boolean poss = true;
                    int num = 0;

                    for(int l=0;l<arr.length;l++) {
                        int min = Integer.MAX_VALUE;
                        num = arr[l];
                        for(int a=0;a<=j;a++) {
                            for(int b=0;b<=k;b++) {
                                int rem = arr[l] - 1*a -2*b;
                                if(rem >= 0 && rem%3 == 0) {
                                    min = Math.min(min, rem/3);
                                }
                            }
                        }

                        if(min != Integer.MAX_VALUE) {
                            coins = Math.max(coins, min);
                        }else {
                            poss = false;
                            break;
                        }
                    }

                    //System.out.println("isPoss for "+  num + " " + poss + " ones-" + j + " twos-" + k + " threes-" + coins);

                    if(!poss) {
                        continue;
                    }else {
                        total = Math.min(total, coins+j+k);
                    }

                }
            }

            printNumber(total);

        }

        out.flush();

    }

     public static int ub(long[] arr, long num) {
        int start = 0;
        int end = arr.length;
        int mid = 0;

        while(start<end) {
            mid = start + (end-start)/2;
            if(arr[mid] < num) {
                start = mid+1;
            }else {
                end = mid;
            }
        }
        return start;
     }

    public static int[] convertToIntPrimitiveArray() throws IOException {
        String[] str = reader.readLine().split(" ");
        return Stream.of(str).mapToInt(Integer::parseInt).toArray();
    }

    public static Integer[] convertToIntArray(String[] str) {
        Integer[] arr = new Integer[str.length];
        for(int i=0;i<str.length;i++) {
            arr[i] = Integer.parseInt(str[i]);
        }
        return arr;
    }

    public static Long[] convertToLongArray(String[] str) {
        Long[] arr = new Long[str.length];
        for(int i=0;i<str.length;i++) {
            arr[i] = Long.parseLong(str[i]);
        }
        return arr;
    }

    public static long[] convertToLongPrimitiveArray() throws IOException {
        String[] str = reader.readLine().split(" ");
        return Stream.of(str).mapToLong(Long::parseLong).toArray();
    }

    public static void printYes() throws IOException {
        out.append("YES" + "\n");
    }

    public static void printNo() throws IOException {
        out.append("NO" + "\n");
    }

    public static void printNumber(long num) throws IOException {
        out.append(num + "\n");
    }

    public static long hcf(long a, long b) {
        if(b==0) return a;
        return hcf(b, a%b);
    }

    public static int findSet(int[] parent, int[] rank, int v) {
        if(v==parent[v]) {
            return v;
        }
        parent[v] = findSet(parent, rank, parent[v]);
        return parent[v];
    }

    public static void unionSet(int[] parent, int[] rank, int a, int b) {

        a = findSet(parent, rank, a);
        b = findSet(parent, rank, b);

        if(a == b) {
            return;
        }

        if(rank[a] < rank[b]) {
            int temp = a;
            a = b;
            b = temp;
        }

        parent[b] = a;
        if(rank[a] == rank[b]) {
            rank[a]++;
        }

    }

    public static void makeSet(int[] parent, int[] rank, int v) {
        parent[v] = v;
        rank[v] = 0;
    }

    public static long modularDivision(long a, long b, int mod) {
        if(a==0) return 1;
        a %= mod;
        long res = 1L;
        while(b > 0) {
            if((b&1)==1) {
                res = (res * a)%mod;
            }
            a = (a*a)%mod;
            b >>= 1;
        }
        return res;
    }

    public static void customSort(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        Arrays.sort(arr);
        return;
    }

    public static void customSortLong(long[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        Arrays.sort(arr);
        return;
    }

    public static long[] factorial(int n, int mod) {
        long[] fact = new long[n+1];
        fact[0] = 1;
        for(int i=1;i<fact.length;i++) {
            fact[i] = (i*fact[i-1] + mod)%mod;
        }
        return fact;
    }

    public static long[] invfactorial(int n, int mod, long[] fact) {
        long[] invfact = new long[n+1];
        invfact[0] = 1L;
        for(int i=1;i<=n;i++) {
            invfact[i] = modularDivision(fact[i], mod-2, mod);
        }
        return invfact;
    }

    public static List<Integer> primeNumbers(int num) {
        boolean[] arr = new boolean[num+1];
        List<Integer> primes = new ArrayList<>();

        for(int i=2;i*i<=num;i++) {
            if(!arr[i]) {
                for(int j=i;j*i<=num;j++) {
                    arr[j*i] = true;
                }
            }
        }

        for(int i=2;i<=num;i++) {
            if(!arr[i]) {
                primes.add(i);
            }
        }
        return primes;
    }

    public static long ncr(int n, int r, long mod, long[] fact, long[] invfact) {
        if(n<0 || r<0 || n < r) {
            return 0;
        }
        long temp = (fact[n]*invfact[n-r])%mod;
        temp = (temp*invfact[r])%mod;
        return temp;
    }


}