import java.io.*;
import java.util.*;
import java.util.StringTokenizer;
import javafx.util.Pair;

public class Deep_Down_Below
{
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

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

        public Reader(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]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    }
                    else {
                        continue;
                    }
                }
                buf[cnt++] = (byte)c;
            }
            return new String(buf, 0, cnt);
        }

        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++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
    public static long gcd (long a, long b)
    {
        if (b == 0)
        {
            return a;
        }
        return gcd (b, a % b);
    }
    public static long lcm (long a, long b)
    {
        long hcf = gcd (a, b);
        return (a * b) / hcf;
    }
    public static void SortByColumn (long arr[][])
    {
        Arrays.sort (arr, new Comparator<long[]> () {
            public int compare (long[] arr1, long[] arr2)
            {
                if (arr1[0] > arr2[0])
                {
                    return 1;
                }
                else if (arr1[0] < arr2[0])
                {
                    return -1;
                }
                else
                {
                    if (arr1[1] > arr2[1])
                    {
                        return 1;
                    }
                    else
                    {
                        return -1;
                    }
                }
            }
        });
    }
    public static long sqrtl (long n)
    {
        long low = 0, high = (long)1e10, ans = -1;
        while (low <= high)
        {
            long mid = (low + high) / 2;
            if (mid * mid <= n)
            {
                ans = mid;
                low = mid + 1;
            }
            else
            {
                high = mid - 1;
            }
        }
        return ans;
    }
    public static boolean func (long[][] arr, long num)
    {
        int n = arr.length, i;
        for (i=0;i<n;i++)
        {
            if (num >= arr[i][0])
            {
                num += arr[i][1];
            }
            else
            {
                return false;
            }
        }
        return true;
    }
    public static PrintWriter out;
    public static void main (String[] args) throws java.lang.Exception
    {
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        /*try
        {*/
            //Scanner obj = new Scanner (System.in);
            Reader obj = new Reader ();
            int t = obj.nextInt();
            while (t > 0)
            {
                t--;
                int n = obj.nextInt();
                //long n = obj.nextLong();
                //String str = obj.next();
                //char ch[] = str.toCharArray();
                //int arr[] = new int[n];
                long arr[][] = new long[n][2];
                //ArrayList<Integer> arr = new ArrayList<Integer>(n);
                //ArrayList<Long> arr = new ArrayList<Long>(n);
                //HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
                //HashMap<Long, Long> map = new HashMap<Long, Long>();
                //Set<Integer> set = new HashSet<Integer>();
                //Set<Long> set = new HashSet<Long>();
                //Set<Character> set = new HashSet<Character>();
                int i, j;
                for (i=0;i<n;i++)
                {
                    long k = obj.nextLong();
                    long max = -1;
                    for (j=0;j<k;j++)
                    {
                        long num = obj.nextLong();
                        max = Math.max (max, num + 1 - j);
                    }
                    arr[i][0] = max;
                    arr[i][1] = k;
                }
                SortByColumn (arr);
                long low = 0, high = (long)1e10, ans = -1;
                while (low <= high)
                {
                    long mid = (low + high) / 2;
                    if (func (arr, mid))
                    {
                        ans = mid;
                        high = mid - 1;
                    }
                    else
                    {
                        low = mid + 1;
                    }
                }
                out.println (ans);
            }
        /*}catch(Exception e){
            return;
        }*/
        out.flush();
        out.close();
    }
}