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.*;
import java.util.*;

public class Main {
    class JoinSet {
        int[] fa;
        JoinSet(int n){
            fa = new int[n];
            for(int i = 0;i < n;i++) fa[i] = i;
        }
        int find(int x){
            if(x != fa[x]) fa[x] = find(fa[x]);
            return fa[x];
        }
        void join(int x, int y){
            x = find(x);
            y = find(y);
            fa[x] = y;
        }
    }
    static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static int mod = (int)1e9+7;
    static boolean[] isprime=new boolean[1];
    static {
        for(int i=2;i<isprime.length;i++) isprime[i]=true;
        for(int i=2;i<isprime.length;i++) {
            if(isprime[i]) {
                for(int k = 2; i*k<isprime.length; k++) {
                    isprime[i*k] = false;
                }
            }
        }
    }
    public static long gcd(long a, long b){
        return b == 0 ? a : gcd(b,a%b);
    }
    public static long lcm(long a, long b){
        return a*b / gcd(a,b);
    }
    public static int get() throws Exception{
        String ss = bf.readLine();
        if (ss.contains(" ")) ss = ss.substring(0, ss.indexOf(" "));
        return Integer.parseInt(ss);
    }
    public static int[] getInt() throws Exception {
        String s[] = bf.readLine().split(" ");
        int[] a = new int[s.length];
        for(int i = 0;i < a.length;i++){
            a[i] = Integer.parseInt(s[i]);
        }
        return a;
    }
    public static long[] getLong() throws Exception {
        String s[] = bf.readLine().split(" ");
        long[] a = new long[s.length];
        for(int i = 0;i < a.length;i++){
            a[i] = Long.parseLong(s[i]);
        }
        return a;
    }
    public static void print(int[] a) throws Exception {
        for(int i : a){
            bw.write(i + " ");
        }
        println();
    }
    public static void print(long[] a) throws Exception {
        for(long i : a){
            bw.write(i + " ");
        }
        println();
    }
    public static void println() throws Exception{
        bw.write("\n");
    }
    public static long pow(long a, long b){
        long ans = 1;
        while(b > 0){
            if((b&1) == 1){
                ans *= a;
            }
            a*=a;
            b>>=1;
        }
        return ans;
    }
    public static int powmod(long a, long b, int mod){
        long ans = 1;
        while(b > 0){
            if((b&1) == 1){
                ans = ans * a % mod;
            }
            a = a * a % mod;
            b>>=1;
        }
        return (int)ans;
    }
    public static void sort(int[] a){
        int n = a.length;
        Integer[] b = new Integer[n];
        for(int i = 0;i < n;i++) b[i] = a[i];
        Arrays.sort(b);
        for(int i = 0;i < n;i++) a[i] = b[i];
    }

    public static void main(String[] args) throws Exception {
        int t = get();
        while (t-- > 0){
            int n = get();
            int[] a = getInt();
            int max = Arrays.stream(a).max().getAsInt();
            int ans = 0;
            boolean f = false, f1 = false, f2 = false;
            for(int i = 0;i < n;i++){
                if(a[i] == max-1) f = true;
                if(a[i] != max && a[i] % 3 == 2) f2 = true;
                if(a[i] != max && a[i] % 3 == 1) f1 = true;
            }
            if(max % 3 == 0){
                ans = max/3;
                if(f2 || f1)  ans = max/3+1;
            }else if(max % 3 == 1){
                ans = max/3+1;
                if((f2 && f1) || f)  ans = max/3+2;
            }else{
                ans = max/3+1;
                if(f1)  ans = max/3+2;
            }
            bw.write(ans+"\n");
        }
        bw.flush();
    }
}
