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.Arrays;

public class D {
    public static void main(String[] args) throws IOException {
        FastScanner scanner = new FastScanner();
        int t = scanner.nextInt();
        while (t-- > 0) {
            int n = scanner.nextInt();
            int[] a = new int[n];
            int max = Integer.MIN_VALUE;
            boolean remainder1 = false, remainder2 = false, hasOne = false;
            for (int i = 0; i < n; i++) {
                a[i] = scanner.nextInt();
                if (a[i] % 3 == 1) remainder1 = true;
                else if (a[i] % 3 == 2) remainder2 = true;
                if (a[i] == 1) hasOne = true;
                max = Math.max(max, a[i]);
            }


            if (max % 3 == 0) {
                if (remainder1 || remainder2) {
                    System.out.println(max / 3 + 1);
                } else {
                    System.out.println(max / 3);
                }
            } else if (max % 3 == 1) {
                if (!remainder2) {
                    System.out.println(max / 3 + 1);
                } else {
                    boolean hasMaxMinusOne = false;
                    for (int i : a)
                        if (i == max - 1) { hasMaxMinusOne = true; break; }
                    System.out.println(max / 3 + (hasMaxMinusOne ? 2 : 1));
                }
            } else {  // max % 3 == 2
                if (remainder1) {
                    System.out.println(max / 3 + 2);
                } else {
                    System.out.println(max / 3 + 1);
                }
            }
        }
    }

    /**
     * Credits: https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
     */
    private static class FastScanner implements Closeable {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastScanner() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastScanner(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n' || c == '\r') {
                    if (cnt != 0) {
                        break;
                    } else {
                        continue;
                    }
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String next() throws IOException {
            return next(32);
        }

        public String next(int len) throws IOException {
            byte[] buf = new byte[len];
            int ptr = 0;
            byte c = read();
            while (c <= ' ') c = read();
            do {
                if (ptr == buf.length) {
                    buf = Arrays.copyOf(buf, buf.length << 1);
                }
                buf[ptr++] = c;
            } while ((c = read()) > ' ');
            if (buf.length == ptr) return new String(buf);
            return new String(Arrays.copyOf(buf, ptr));
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        @Override
        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }
}
