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 Main {
    static FastScanner sc = new FastScanner(System.in);
    static PrintWriter pw = new PrintWriter(System.out);
    static StringBuilder sb = new StringBuilder();
    static long mod = (long) 1e9 + 7;

    public static void main(String[] args) throws Exception {
        int n = sc.nextInt();
        for(int i = 0; i < n; i++) solve();
        pw.flush();
    }

    public static void solve() {
        int n = sc.nextInt();
        ArrayList<Integer> arr = new ArrayList<>();
        for(int i = 0; i < n; i++){
            arr.add(sc.nextInt());
        }
        Collections.sort(arr,Comparator.reverseOrder());
        boolean mod1 = false;
        boolean mod2 = false;
        for(int i = 1; i < n; i++){
            if(arr.get(i) % 3 == 2){
                mod2 = true;
            }else if(arr.get(i) % 3 == 1){
                mod1 = true;
            }
        }
        int max = arr.get(0)/3;
        if(arr.get(0) % 3 != 0) max++;
        if(arr.get(0) % 3 == 2){
            mod2 = false;
        }else if(arr.get(0) % 3 == 1){
            mod1 = false;
        }
        if(mod1 && mod2){
            pw.println(max+1);
        }else if((mod1 || mod2) && arr.get(0) < 7){
            pw.println(max+1);
        }else{
            pw.println(max);
        }
        sb.setLength(0);
    }

    static class GeekInteger {
        public static void save_sort(int[] array) {
            shuffle(array);
            Arrays.sort(array);
        }

        public static int[] shuffle(int[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                int randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }

        public static void save_sort(long[] array) {
            shuffle(array);
            Arrays.sort(array);
        }

        public static long[] shuffle(long[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                long randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }

    }
}

class DSU {
	private int n;
	private int[] parentOrSize;

	public DSU(int n) {
		this.n = n;
		this.parentOrSize = new int[n];
		java.util.Arrays.fill(parentOrSize, -1);
	}

	int merge(int a, int b) {
		if (!(0 <= a && a < n))
			throw new IndexOutOfBoundsException("a=" + a);
		if (!(0 <= b && b < n))
			throw new IndexOutOfBoundsException("b=" + b);

		int x = leader(a);
		int y = leader(b);
		if (x == y)
			return x;
		if (-parentOrSize[x] < -parentOrSize[y]) {
			int tmp = x;
			x = y;
			y = tmp;
		}
		parentOrSize[x] += parentOrSize[y];
		parentOrSize[y] = x;
		return x;
	}

	boolean same(int a, int b) {
		if (!(0 <= a && a < n))
			throw new IndexOutOfBoundsException("a=" + a);
		if (!(0 <= b && b < n))
			throw new IndexOutOfBoundsException("b=" + b);
		return leader(a) == leader(b);
	}

	int leader(int a) {
		if (parentOrSize[a] < 0) {
			return a;
		} else {
			parentOrSize[a] = leader(parentOrSize[a]);
			return parentOrSize[a];
		}
	}

	int size(int a) {
		if (!(0 <= a && a < n))
			throw new IndexOutOfBoundsException("" + a);
		return -parentOrSize[leader(a)];
	}

	java.util.ArrayList<java.util.ArrayList<Integer>> groups() {
		int[] leaderBuf = new int[n];
		int[] groupSize = new int[n];
		for (int i = 0; i < n; i++) {
			leaderBuf[i] = leader(i);
			groupSize[leaderBuf[i]]++;
		}
		java.util.ArrayList<java.util.ArrayList<Integer>> result = new java.util.ArrayList<>(n);
		for (int i = 0; i < n; i++) {
			result.add(new java.util.ArrayList<>(groupSize[i]));
		}
		for (int i = 0; i < n; i++) {
			result.get(leaderBuf[i]).add(i);
		}
		result.removeIf(java.util.ArrayList::isEmpty);
		return result;
	}
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;

    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public FastScanner(FileReader in) {
        reader = new BufferedReader(in);
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    }
}
