description: In a certain video game, the player controls a hero characterized by a single integer value: power. The hero will have to beat monsters that are also characterized by a single integer value: armor.
  
  On the current level, the hero is facing n caves. To pass the level, the hero must enter all the caves in some order, each cave exactly once, and exit every cave safe and sound. When the hero enters cave i, he will have to fight k_i monsters in a row: first a monster with armor a_{i, 1}, then a monster with armor a_{i, 2} and so on, finally, a monster with armor a_{i, k_i}.
  
  The hero can beat a monster if and only if the hero's power is strictly greater than the monster's armor. If the hero can't beat the monster he's fighting, the game ends and the player loses. Note that once the hero enters a cave, he can't exit it before he fights all the monsters in it, strictly in the given order.
  
  Each time the hero beats a monster, the hero's power increases by 1.
  
  Find the smallest possible power the hero must start the level with to be able to enter all the caves in some order and beat all the monsters.
  
  Input
  
  Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^5). Description of the test cases follows.
  
  The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the number of caves.
  
  The i-th of the next n lines contains an integer k_i (1 ≤ k_i ≤ 10^5) — the number of monsters in the i-th cave, followed by k_i integers a_{i, 1}, a_{i, 2}, …, a_{i, k_i} (1 ≤ a_{i, j} ≤ 10^9) — armor levels of the monsters in cave i in order the hero has to fight them.
  
  It is guaranteed that the sum of k_i over all test cases does not exceed 10^5.
  
  Output
  
  For each test case print a single integer — the smallest possible power the hero must start the level with to be able to enter all the caves in some order and beat all the monsters.
  
  Example
  
  Input
  
  
  2
  1
  1 42
  2
  3 10 15 8
  2 12 11
  
  
  Output
  
  
  43
  13
  
  Note
  
  In the first test case, the hero has to beat a single monster with armor 42, it's enough to have power 43 to achieve that.
  
  In the second test case, the hero can pass the level with initial power 13 as follows: 
  
    * enter cave 2: 
      * beat a monster with armor 12, power increases to 14; 
      * beat a monster with armor 11, power increases to 15; 
    * enter cave 1: 
      * beat a monster with armor 10, power increases to 16; 
      * beat a monster with armor 15, power increases to 17; 
      * beat a monster with armor 8, power increases to 18. 
solution: import java.io.BufferedReader;
  import java.io.BufferedWriter;
  import java.io.File;
  import java.io.FileReader;
  import java.io.FileWriter;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.OutputStreamWriter;
  import java.io.PrintWriter;
  import java.lang.reflect.Array;
  import java.util.ArrayDeque;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.Comparator;
  import java.util.Deque;
  import java.util.HashMap;
  import java.util.HashSet;
  import java.util.LinkedHashMap;
  import java.util.LinkedList;
  import java.util.List;
  import java.util.Map;
  import java.util.PriorityQueue;
  import java.util.Queue;
  import java.util.Random;
  import java.util.Set;
  import java.util.Stack;
  import java.util.StringTokenizer;
  import java.util.TreeSet;
  import java.util.stream.Collectors;
  
  public class Main {
      static int mod = (int) (1e9) + 7;
  
      /* ======================DSU===================== */
      static class dsu {
          static int parent[], n;// min[],value[];
          static long size[];
  
          dsu(int n) {
              parent = new int[n + 1];
              size = new long[n + 1];
              // min=new int[n+1];
              // value=new int[n+1];
              Main.dsu.n = n;
              makeSet();
          }
  
          static void makeSet() {
              for (int i = 1; i <= n; i++) {
                  parent[i] = i;
                  size[i] = 1;
                  // min[i]=i;
              }
          }
  
          static int find(int a) {
              if (parent[a] == a)
                  return a;
              else {
                  return parent[a] = find(parent[a]);// Path Compression
              }
          }
  
          static void union(int a, int b) {
              int setA = find(a);
              int setB = find(b);
              if (setA == setB)
                  return;
              if (size[setA] >= size[setB]) {
                  parent[setB] = setA;
                  size[setA] += size[setB];
              } else {
                  parent[setA] = setB;
                  size[setB] += size[setA];
              }
          }
      }
  
      /* ======================================================== */
      static class Pair<X extends Number, Y extends Number> implements Comparator<Pair> {
          X x;
          Y y;
  
          // Constructor
          public Pair(X x, Y y) {
              this.x = x;
              this.y = y;
          }
  
          public Pair() {
  
          }
  
          @Override
          public int compare(Main.Pair o1, Main.Pair o2) {
              return ((int) (o1.y.intValue() - o2.y.intValue()));// Ascending Order based on 'y'
          }
      }
  
      /* ===============================Tries================================= */
      static class TrieNode {
          private HashMap<Character, TrieNode> children = new HashMap<>();
          public int size;
          boolean endOfWord;
  
          public void putChildIfAbsent(char ch) {
              children.putIfAbsent(ch, new TrieNode());
          }
  
          public TrieNode getChild(char ch) {
              return children.get(ch);
          }
      }
  
      static private TrieNode root;
  
      public static void insert(String str) {
          TrieNode curr = root;
          for (char ch : str.toCharArray()) {
              curr.putChildIfAbsent(ch);
              curr = curr.getChild(ch);
              curr.size++;
          }
          // mark the current nodes endOfWord as true
          curr.endOfWord = true;
      }
  
      public static int search(String word) {
          TrieNode curr = root;
  
          for (char ch : word.toCharArray()) {
              curr = curr.getChild(ch);
              if (curr == null) {
                  return 0;
              }
          }
          // size contains words starting with prefix- word
          return curr.size;
      }
  
      public boolean delete(TrieNode current, String word, int index) {
          if (index == word.length()) {
              // when end of word is reached only delete if currrent.endOfWord is true.
              if (!current.endOfWord) {
                  return false;
              }
              current.endOfWord = false;
              // if current has no other mapping then return true
              return current.children.size() == 0;
          }
          char ch = word.charAt(index);
          TrieNode node = current.children.get(ch);
          if (node == null) {
              return false;
          }
          boolean shouldDeleteCurrentNode = delete(node, word, index + 1);
  
          // if true is returned then delete the mapping of character and trienode
          // reference from map.
          if (shouldDeleteCurrentNode) {
              current.children.remove(ch);
              // return true if no mappings are left in the map.
              return current.children.size() == 0;
          }
          return false;
      }
  
      /* ================================================================= */
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
  
          double nextDouble() {
              return Double.parseDouble(next());
          }
  
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          int[] intArr(int n) {
              int res[] = new int[n];
              for (int i = 0; i < n; i++)
                  res[i] = nextInt();
              return res;
          }
  
          long[] longArr(int n) {
              long res[] = new long[n];
              for (int i = 0; i < n; i++)
                  res[i] = nextLong();
              return res;
          }
      }
  
      static FastReader f = new FastReader();
      static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));
  
      static boolean isPrime(long n) {
          if (n <= 1)
              return false;
          if (n <= 3)
              return true;
          if (n % 2 == 0 || n % 3 == 0)
              return false;
          for (long i = 5; i * i <= n; i = i + 6)
              if (n % i == 0 || n % (i + 2) == 0)
                  return false;
          return true;
      }
  
      static int lowerBound(int a[], int x) { // x is the target, returns lowerBound. If not found return -1
          int l = -1, r = a.length, flag = 0;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (x == a[m])
                  flag = 1;
              if (a[m] >= x)
                  r = m;
              else
                  l = m;
          }
          return r;
      }
  
      static int upperBound(int a[], int x, int l, int r) {// x is the target, returns upperBound. If not found return -1
          int flag = 0;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a[m] == x)
                  return m;
              if (a[m] <= x) {
                  l = m;
                  flag = 1;
              } else
                  r = m;
          }
          return l + 1;
      }
  
      static long gcd(long a, long b) {
          if (a == 0)
              return b;
          return gcd(b % a, a);
      }
  
      static long lcm(long a, long b) {
          return (a * b) / gcd(a, b);
      }
  
      static long power(long x, long y) {
          long res = 1;
          while (y > 0) {
              if (y % 2 == 1)
                  res = (res * x);
              y >>= 1;
              x = (x * x);
          }
          return res;
      }
  
      public double binPow(double x, int n) {// binary exponentiation with negative power as well
          if (n == 0)
              return 1.0;
          double binPow = binPow(x, n / 2);
          if (n % 2 == 0) {
              return binPow * binPow;
          } else {
              return n > 0 ? (binPow * binPow * x) : (binPow * binPow / x);
          }
      }
  
      static long ceil(long x, long y) {
          return (x % y == 0 ? x / y : (x / y + 1));
      }
  
      /*
       * ===========Modular Operations==================
       */
      static long modPower(long x, long y, long p) {
          long res = 1;
          x = x % p;
          while (y > 0) {
              if (y % 2 == 1)
                  res = (res * x) % p;
              y = y >> 1; // y = y/2
              x = (x * x) % p;
          }
          return res;
      }
  
      static long modInverse(long n, long p) {
          return modPower(n, p - 2, p);
      }
  
      static long modAdd(long a, long b) {
          return ((a + b + mod) % mod);
      }
  
      static long modMul(long a, long b) {
          return ((a % mod) * (b % mod)) % mod;
      }
  
      static long[] fac = new long[200000 + 5];
      static long[] invFac = new long[200000 + 5];
  
      static long nCrModPFermat(int n, int r) {
          if (r == 0)
              return 1;
          // return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod)
          // % mod) % mod;
          return (fac[n] * invFac[r] % mod * invFac[n - r] % mod) % mod;
      }
  
      /*
       * ===============================================
       */
  
      static void ruffleSort(long[] a) {
          int n = a.length;
          Random r = new Random();
          for (int i = 0; i < a.length; i++) {
              int oi = r.nextInt(n);
              long temp = a[i];
              a[i] = a[oi];
              a[oi] = temp;
          }
          Arrays.sort(a);
      }
  
      static void ruffleSort(int[] a) {
          int n = a.length;
          Random r = new Random();
          for (int i = 0; i < a.length; i++) {
              int oi = r.nextInt(n);
              int temp = a[i];
              a[i] = a[oi];
              a[oi] = temp;
          }
          Arrays.sort(a);
      }
  
      static String binString32(int n) {
          StringBuilder str = new StringBuilder("");
          String bin = Integer.toBinaryString(n);
          if (bin.length() != 32) {
              for (int k = 0; k < 32 - bin.length(); k++) {
                  str.append("0");
              }
              str.append(bin);
          }
          return str.toString();
      }
  
      static class sparseTable {
          public static int st[][];
          public static int log = 4;
  
          static int func(int a, int b) {// make func as per question(here min range query)
              return (int) gcd(a, b);
          }
  
          void makeTable(int n, int a[]) {
  
              st = new int[n][log];
              for (int i = 0; i < n; i++) {
                  st[i][0] = a[i];
              }
              for (int j = 1; j < log; j++) {
                  for (int i = 0; i + (1 << j) <= n; i++) {
                      st[i][j] = func(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
                  }
              }
          }
  
          static int query(int l, int r) {
              int length = r - l + 1;
              int k = 0;
              while ((1 << (k + 1)) <= length) {
                  k++;
              }
              return func(st[l][k], st[r - (1 << k) + 1][k]);
          }
  
          static void printTable(int n) {
              for (int j = 0; j < log; j++) {
                  for (int i = 0; i < n; i++) {
                      System.out.print(st[i][j] + " ");
                  }
                  System.out.println();
              }
          }
      }
  
      /*
       * ====================================Main=================================
       */
  
      // static int st[], a[];
  
      // static void buildTree(int treeIndex, int lo, int hi) {
      // if (hi == lo) {
      // st[treeIndex] = a[lo];
      // return;
      // }
      // int mid = (lo + hi) / 2;
      // buildTree(treeIndex * 2 + 1, lo, mid);
      // buildTree(treeIndex * 2 + 2, mid + 1, hi);
      // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
      // }
  
      // static void update(int treeIndex, int lo, int hi, int arrIndex, int val) {
      // if (hi == lo) {
      // st[treeIndex] = val;
      // a[arrIndex] = val;
      // return;
      // }
      // int mid = (hi + lo) / 2;
      // if (mid < arrIndex) {
      // update(treeIndex * 2 + 2, mid + 1, hi, arrIndex, val);
      // } else {
      // update(treeIndex * 2 + 1, lo, mid, arrIndex, val);
      // }
      // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
      // }
  
      // static int query(int treeIndex, int lo, int hi, int l, int r) {
      // if (l <= lo && r >= hi) {
      // return st[treeIndex];
      // }
      // if (l > hi || r < lo) {
      // return 0;
      // }
      // int mid = (hi + lo) / 2;
      // return query(treeIndex * 2 + 1, lo, mid, l, Math.min(mid, r));
      // }
  
      // static int merge(int a, int b) {
      // return a + b;
      // }
  
      public static long findKthPositive(long[] A, long k) {
          int l = 0, r = A.length, m;
          while (l < r) {
              m = (l + r) / 2;
              if (A[m] - 1 - m < k)
                  l = m + 1;
              else
                  r = m;
          }
          return l + k;
      }
  
      static int[] z_function(char ar[]) {
          int[] z = new int[ar.length];
          z[0] = ar.length;
          int l = 0;
          int r = 0;
          for (int i = 1; i < ar.length; i++) {
              if (r < i) {
                  l = i;
                  r = i;
                  while (r < ar.length && ar[r - l] == ar[r])
                      r++;
                  z[i] = r - l;
                  r--;
              } else {
                  int k = i - l;
                  if (z[k] < r - i + 1) {
                      z[i] = z[k];
                  } else {
                      l = i;
                      while (r < ar.length && ar[r - l] == ar[r])
                          r++;
                      z[i] = r - l;
                      r--;
                  }
              }
          }
          return z;
      }
  
      static void mergeSort(int a[]) {
          int n = a.length;
          if (n >= 2) {
              int mid = n / 2;
              int left[] = new int[mid];
              int right[] = new int[n - mid];
              for (int i = 0; i < mid; i++) {
                  left[i] = a[i];
              }
              for (int i = mid; i < n; i++) {
                  right[i - mid] = a[i];
              }
              mergeSort(left);
              mergeSort(right);
              mergeSortedArray(left, right, a);
          }
      }
  
      static void mergeSortedArray(int left[], int right[], int a[]) {
          int i = 0, j = 0, k = 0, n = left.length, m = right.length;
          while (i != n && j != m) {
              if (left[i] < right[j]) {
                  a[k++] = left[i++];
              } else {
                  a[k++] = right[j++];
              }
          }
          while (i != n) {
              a[k++] = left[i++];
          }
          while (j != m) {
              a[k++] = right[j++];
          }
      }
  
      // BINARY SEARCH
      // count of set bits in a particular position
      // suffix max array/ suffix sum array/ prefix
      static int min;
  
      static class Data {
          int num, max;
          ArrayList<Integer> armour;
  
          Data(int num, int max, ArrayList<Integer> a) {
              this.num = num;
              this.max = max;
              armour = new ArrayList<>(a);
          }
      }
  
      public static void main(String args[]) throws Exception {
          int t = 1;
          t = f.nextInt();
          int tc = 1;
          // fac[0] = 1;
          // for (int i = 1; i <= 200000; i++) {
          // fac[i] = fac[i - 1] * i % mod;
          // invFac[i] = modInverse(fac[i], mod);
          // }
          while (t-- != 0) {
              int n = f.nextInt();
              ArrayList<Data> a = new ArrayList<>();
              for (int i = 0; i < n; i++) {
                  int k = f.nextInt();
                  int max = 0;
                  ArrayList<Integer> ar = new ArrayList<>();
                  for (int j = 0; j < k; j++) {
                      int q = f.nextInt();
                      ar.add(q);
                      max = Math.max(max,q-j);
                  }
                  a.add(new Data(k, max, ar));
                  // System.out.println(a.get(i).armour.get(a.get(i).max));
              }
              Collections.sort(a, (p, q) -> (p.max - q.max)!=0?(p.max-q.max):(p.num-q.num));
              // for(int i=0;i<n;i++){
              //     for(int j:a.get(i).armour){
              //         w.write(j+" ");
              //     }
              //     w.write("\n");
              // }
              long maxStrength = 0;
              long lo = 1, hi = (long)1e10;
              while (hi >= lo) {
                  long mid = lo + (hi - lo) / 2;
                  long currStrength = mid;
                  int flag = 1;
                  for (int i = 0; i < n; i++) {
                      for (int j = 0; j < a.get(i).num; j++) {
                          if (currStrength > a.get(i).armour.get(j)) {
                              currStrength++;
                          } else {
                              flag = 0;
                              break;
                          }
                      }
                      if (flag == 0)
                          break;
                  }
                  if (flag == 1) {
                      maxStrength = mid;
                      hi = mid - 1;
                  } else {
                      lo = mid + 1;
                  }
              }
              w.write(maxStrength + "\n");
          }
          w.flush();
      }
  }
  /*
  8 2 9 10 3 
  3 4 5 12 13 11 14 12 
  10 2 1 1 12 11 1 11 
  5 12 1 10 13 5 11 
  13 1 8 5 
  14 
  14 2 
  5 15 11 4 5 
  8 9 16 7 3 6 
  9
  */