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 D {

	static FastScanner fs = new FastScanner();
	static Scanner scn = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
	static StringBuilder sb = new StringBuilder("");
	static int INF = 2147483449;
	
	public static void main(String[] args) {
		int t = fs.nextInt();
		for (int tt = 0; tt < t; tt++) {
			int n = fs.nextInt();
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = fs.nextInt();
			int ans = INF;
			for (int i = 0; i < 2; i++) {
				for (int j = 0; j < 3; j++) {
					int max = 0;
					for (int k = 0; k < n; k++) {
						int min = INF;
						for (int l = 0; l <= i; l++) {
							for (int o = 0; o <= j; o++) {
								int x = a[k] - l - o * 2;
								if (x % 3 == 0 && x >= 0) min = Math.min(min, x/3);
							}
						}
						max = Math.max(max, min);
					}
					ans = Math.min(ans, max + i + j);
				}
			}
			sb.append(ans + "\n");
		}
		pw.print(sb.toString());
		pw.close();
	}
	
	static class Pair implements Comparable<Pair> {
		char first = 0;
		int second = 0;
		
		Pair(char first, int second) {
			this.first = first;
			this.second = second;
		}
		
		public int compareTo(Pair o) {
			if (second == o.second) return Integer.compare(first, o.first);
			else return Integer.compare(second, o.second);
		}
	}

	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		String next() {
			while (!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
				}
			return st.nextToken();
		}

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

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

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

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