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

/*
Codeforces
Problem 1620D
*/

import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;

public class ExactChange {
	
	public static void main(String[] args) throws IOException {
		FastIO in = new FastIO(System.in);
		
		int t = in.nextInt();
		while (t-- > 0) {
			int n = in.nextInt();
			int[] a = new int[n];
			
			int mod0 = 0;
			int mod1 = 0;
			int mod2 = 0;
			for (int i = 0; i < n; i++) {
				a[i] = in.nextInt();
				if (a[i] % 3 == 0) mod0++;
				else if (a[i] % 3 == 1) mod1++;
				else mod2++;
			}
			Arrays.sort(a);
			
			if (a[n-1] % 3 == 0) {
				System.out.println(mod0 == n ? a[n-1] / 3 : a[n-1] / 3 + 1);
			} else if (a[n-1] % 3 == 1) {
				if (mod2 == 0) System.out.println(a[n-1] / 3 + 1);
				else if (mod0 == 0 && a[0] > 1) System.out.println(a[n-1] / 3 + 1);
				else System.out.println(a[n-1] / 3 + 2);
			} else {
				System.out.println(mod1 == 0 ? a[n-1] / 3 + 1 : a[n-1] / 3 + 2);
			}
		}
		
		in.close();
	}
	
	public static class FastIO {
		private InputStream dis;
		private byte[] buffer = new byte[1 << 17];
		private int pointer = 0;
	
		public FastIO(String fileName) throws IOException {
			dis = new FileInputStream(fileName);
		}
	
		public FastIO(InputStream is) throws IOException {
			dis = is;
		}
	
		public int nextInt() throws IOException {
			int ret = 0;
			byte b;
			
			do {
				b = nextByte();
			} while (b <= ' ');
			
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
	
			return (negative) ? -ret : ret;
		}
	
		public long nextLong() throws IOException {
			long ret = 0;
			byte b;
			
			do {
				b = nextByte();
			} while (b <= ' ');
			
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
			
			return (negative) ? -ret : ret;
		}
	
		public byte nextByte() throws IOException {
			if (pointer == buffer.length) {
				dis.read(buffer, 0, buffer.length);
				pointer = 0;
			}
			return buffer[pointer++];
		}
	
		public String next() throws IOException {
			StringBuffer ret = new StringBuffer();
			byte b;
			
			do {
				b = nextByte();
			} while (b <= ' ');
			
			while (b > ' ') {
				ret.appendCodePoint(b);
				b = nextByte();
			}
	
			return ret.toString();
		}
	
		public void close() throws IOException {
			dis.close();
		}
	}
}