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 D {
    public static void main(String[] args) throws IOException{
        FastIO file = new FastIO();
        int t = file.nextInt();
        for (int i=0; i<t; i++){
            int n = file.nextInt();
            int[] arr = new int[n];
            for (int j=0; j<n; j++){
                arr[j] = file.nextInt();
            }
            file.println(solve(n, arr));
        }
        file.close();
    }
    public static int solve(int n, int[] arr){
        int max = 0;
        for (int i=0; i<n; i++){
            max = Math.max(max, arr[i]);
        }
        int ans =(int)Math.ceil((double)max/3)+1;
        // Brute force c1 and c2
        for (int c1=0; c1<3; c1++){
            for (int c2=0; c2<3; c2++){
                int c3 = (int)Math.ceil((double)(max-c1-c2*2)/3);
                if (good(c1, c2, c3, arr)){
                    ans = Math.min(ans, c1+c2+c3);
                    if (ans == 2){
                        good(c1, c2, c3, arr);
                    }
                }
            }
        }
        return ans;
    }
    public static boolean good(int c1, int c2, int c3, int[] arr){
        for (int i=0; i<arr.length; i++){
            int curr = arr[i];
            if (curr/3 <= c3){
                curr -= (curr/3)*3;
            }else{
                curr -= c3*3;
            }
            if (curr/2 <= c2){
                curr -= (curr/2)*2;
            }else{
                curr -= c2*2;
            }
            if (curr > c1){
                return false;
            }
        }
        return true;
    }
    static class FastIO extends PrintWriter {
        private InputStream stream;
        private byte[] buf = new byte[1<<16];
        private int curChar, numChars;
    
        public FastIO() { this(System.in,System.out); }
        public FastIO(InputStream i, OutputStream o) {
            super(o);
            stream = i;
        }
        public FastIO(String i, String o) throws IOException {
            super(new FileWriter(o));
            stream = new FileInputStream(i);
        }
        public FastIO(String i) throws IOException {
            super(System.out);
            stream = new FileInputStream(i);
        }
        // throws InputMismatchException() if previously detected end of file
        private int nextByte() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars == -1) return -1; // end of file
            }
            return buf[curChar++];
        }
        // to read in entire lines, replace c <= ' '
        // with a function that checks whether c is a line break
        public String next() {
            int c; do { c = nextByte(); } while (c <= ' ');
            StringBuilder res = new StringBuilder();
            do { res.appendCodePoint(c); c = nextByte(); } while (c > ' ');
            return res.toString();
        }
        public int nextInt() {
            int c; do { c = nextByte(); } while (c <= ' ');
            int sgn = 1; if (c == '-') { sgn = -1; c = nextByte(); }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = 10*res+c-'0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }
        public long nextLong() {
            int c; do { c = nextByte(); } while (c <= ' ');
            int sgn = 1; if (c == '-') { sgn = -1; c = nextByte(); }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = 10*res+c-'0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }
        public double nextDouble() { return Double.parseDouble(next()); }
    }
}