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 Practice {
	static boolean multipleTC = true;
	FastReader in;
	PrintWriter out;

	static int mod = (int) (1e9 + 7);
	int mod2 = 998244353;
	int parent[];
	int rank[];

	public static void main(String[] args) throws Exception {
		new Practice().run();
	}

	void run() throws Exception {
		in = new FastReader();
		out = new PrintWriter(System.out);
		int T = (multipleTC) ? ni() : 1;
		pre();
		for (int t = 1; t <= T; t++)
			solve(t);
		out.flush();
		out.close();
	}

	void pre() throws Exception {
	}

	void solve(int TC) throws Exception {
		int n = ni();
		long arr[] = readArr(n);
		sort(arr);
		long three = 0;
		long one = 0;
		long two = 0;
		for (int i = 0; i < n; i++) {
			// first way
			long need = arr[i];
			if (need % 3 == 0 && two != 1 && one == 1) {
				two++;
				need -= 3;
			}
			need -= (3 * min(three, need / 3));
			if (need % 3 == 0 && one == 1 && two == 1) {
				need -= 3;
			}
			three += (need / 3);
			need %= 3;
			if (need == 2 && two != 1) {
				two++;
			} else if (need == 1 && one != 1) {
				one++;
			}
		}
		long req = one + two + three;
		pn(req);

	}

	void union(int u, int v) {
		u = findParent(u);
		v = findParent(v);
		if (rank[u] > rank[v]) {
			parent[v] = u;
		} else if (rank[u] < rank[v]) {
			parent[u] = v;
		} else {
			parent[v] = u;
			rank[u]++;
		}
	}

	int findParent(int v) {
		if (v == parent[v])
			return v;
		return parent[v] = findParent(parent[v]);
	}

	StringBuilder printArr(int arr[]) {
		StringBuilder sb = new StringBuilder();
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			sb.append(arr[i] + " ");
		}
		return sb;
	}

	StringBuilder printArr(long arr[]) {
		StringBuilder sb = new StringBuilder();
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			sb.append(arr[i] + " ");
		}
		return sb;
	}

	class pair {
		int x, y;

		pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public String toString() {
			return " " + x + ", " + y + "]";
		}

	}

	class pairL {
		long x, y;

		pairL(long x, long y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public String toString() {
			return " " + x + ", " + y + "]";
		}

	}

	boolean isSorted(int arr[]) {
		for (int i = 0; i < arr.length - 1; i++) {
			if (arr[i] > arr[i + 1]) {
				return false;
			}
		}
		return true;
	}

	void swap(int arr[], int x, int y) {
		int t = arr[x];
		arr[x] = arr[y];
		arr[y] = t;
	}

	static int bitCount(int x) {
		return x == 0 ? 0 : (1 + bitCount(x & (x - 1)));
	}

	void sort(long arr[]) {
		ArrayList<Long> list = new ArrayList<>();
		for (int i = 0; i < arr.length; i++)
			list.add(arr[i]);
		Collections.sort(list);
		for (int i = 0; i < arr.length; i++)
			arr[i] = list.get(i);
	}

	static void dbg(Object... o) {
		System.err.println(Arrays.deepToString(o));
	}

	ArrayList<Integer> primeFactorization(int n) {
		ArrayList<Integer> factorization = new ArrayList<>();
		while (n % 2 == 0) {
			factorization.add(2);
			n /= 2;
		}
		for (int d = 3; d * d <= n; d += 2) {
			while (n % d == 0) {
				factorization.add(d);
				n /= d;
			}
		}
		if (n > 1)
			factorization.add(n);
		return factorization;
	}

	private ArrayList<Integer> getPrimes(int n) {
		boolean sieve[] = new boolean[n + 1];
		sieve[0] = sieve[1] = true;
		for (int i = 2; i * i <= n; i++) {
			if (!sieve[i]) {
				for (int j = i * i; j <= n; j += i) {
					sieve[j] = true;
				}
			}
		}
		ArrayList<Integer> primes = new ArrayList<>();
		for (int i = 2; i <= n; i++) {
			if (!sieve[i]) {
				primes.add(i);
			}
		}
		return primes;
	}

	public static boolean isPrime(long n) {
		if (n < 2)
			return false;
		if (n == 2 || n == 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;
		long sqrtN = (long) Math.sqrt(n) + 1;
		for (long i = 6L; i <= sqrtN; i += 6) {
			if (n % (i - 1) == 0 || n % (i + 1) == 0)
				return false;
		}
		return true;
	}

	public static long gcd(long a, long b) {
		if (a > b)
			a = (a + b) - (b = a);
		if (a == 0L)
			return b;
		return gcd(b % a, a);
	}

	public long binaryExpo(long base, long exp) {
		long res = 1;
		while (exp > 0) {
			if ((exp & 1) == 1)
				res = res * base;
			base = base * base;
			exp >>= 1;
		}
		return res;
	}

	public long pow(long base, long exp, long MOD) {
		base %= MOD;
		long res = 1;
		while (exp > 0) {
			if ((exp & 1) == 1)
				res = res * base % MOD;
			base = base * base % MOD;
			exp >>= 1;
		}
		return res;
	}

	public static long totient(long n) {
		long result = n;
		for (int p = 2; p * p <= n; ++p)
			if (n % p == 0) {
				while (n % p == 0)
					n /= p;
				result -= result / p;
			}
		if (n > 1)
			result -= result / n;
		return result;
	}

	int bit(long n) {
		return (n == 0) ? 0 : (1 + bit(n & (n - 1)));
	}

	public long max(long... arr) {
		long max = arr[0];
		for (long itr : arr)
			max = Math.max(max, itr);
		return max;
	}

	public int max(int... arr) {
		int max = arr[0];
		for (int itr : arr)
			max = Math.max(max, itr);
		return max;
	}

	public long min(long... arr) {
		long min = arr[0];
		for (long itr : arr)
			min = Math.min(min, itr);
		return min;
	}

	public int min(int... arr) {
		int min = arr[0];
		for (int itr : arr)
			min = Math.min(min, itr);
		return min;
	}

	public long sum(long... arr) {
		long sum = 0;
		for (long itr : arr)
			sum += itr;
		return sum;
	}

	public long sum(int... arr) {
		long sum = 0;
		for (int itr : arr)
			sum += itr;
		return sum;
	}

	void p(Object o) {
		out.print(o);
	}

	void pn(Object o) {
		out.println(o);
	}

	void pni(Object o) {
		out.println(o);
		out.flush();
	}

	String n() throws Exception {
		return in.next();
	}

	String nln() throws Exception {
		return in.nextLine();
	}

	int ni() throws Exception {
		return Integer.parseInt(in.next());
	}

	long nl() throws Exception {
		return Long.parseLong(in.next());
	}

	long[] readArr(int n) throws Exception {
		long arr[] = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nl();
		}
		return arr;
	}

	double nd() throws Exception {
		return Double.parseDouble(in.next());
	}

	class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastReader(String s) throws Exception {
			br = new BufferedReader(new FileReader(s));
		}

		String next() throws Exception {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new Exception(e.toString());
				}
			}
			return st.nextToken();
		}

		String nextLine() throws Exception {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				throw new Exception(e.toString());
			}
			return str;
		}
	}
}