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.OutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.PrintWriter;
  import java.io.BufferedReader;
  import java.io.InputStreamReader;
  import java.util.*;
  
  public class Main {
      public static void main(String[] args){
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          solve(in, out);
          out.close();
      }
  
      static String reverse(String s) {
          return (new StringBuilder(s)).reverse().toString();
      }
  
      static void sieveOfEratosthenes(int n, int factors[], ArrayList<Integer> ar) 
      { 
          factors[1]=1;
          int p;
          for(p = 2; p*p <=n; p++) 
          { 
              if(factors[p] == 0) 
              { 
                  ar.add(p);
                  factors[p]=p;
                  for(int i = p*p; i <= n; i += p) 
                      if(factors[i]==0)
                          factors[i] = p; 
              } 
          } 
          for(;p<=n;p++){
              if(factors[p] == 0) 
              { 
                  factors[p] = p;
                  ar.add(p);
              } 
          }
      }
  
      static void sort(int ar[]) {
          int n = ar.length;
          ArrayList<Integer> a = new ArrayList<>();
          for (int i = 0; i < n; i++)
              a.add(ar[i]);
          Collections.sort(a);
          for (int i = 0; i < n; i++)
              ar[i] = a.get(i);
      }
  
      static void sort1(long ar[]) {
          int n = ar.length;
          ArrayList<Long> a = new ArrayList<>();
          for (int i = 0; i < n; i++)
              a.add(ar[i]);
          Collections.sort(a);
          for (int i = 0; i < n; i++)
              ar[i] = a.get(i);
      }
  
      static void sort2(char ar[]) {
          int n = ar.length;
          ArrayList<Character> a = new ArrayList<>();
          for (int i = 0; i < n; i++)
              a.add(ar[i]);
          Collections.sort(a);
          for (int i = 0; i < n; i++)
              ar[i] = a.get(i);
      }
  
      static long ncr(long n, long r, long mod) {
          if (r == 0)
              return 1;
          long val = ncr(n - 1, r - 1, mod);
          val = (n * val) % mod;
          val = (val * modInverse(r, mod)) % mod;
          return val;
      }
  
      // static long gcd[];
      
      // static void build(long a[], int v, int tl, int tr) {
      //     if (tl == tr) {
      //         gcd[v] = a[tl];
              
      //     } else {
      //         int tm = (tl + tr) / 2;
      //         build(a, v*2, tl, tm);
      //         build(a, v*2+1, tm+1, tr);
      //         gcd[v] = gcd(gcd[v*2], gcd[v*2+1]);
      //     }
      // }
  
      // static void push(int v, int tl, int tr){
      //     if(tl==tr){
      //         lz[v] = 0;
      //         return;
      //     }
      //     min[2*v] += lz[v];
      //     min[2*v+1] += lz[v];
      //     lz[2*v] += lz[v];
      //     lz[2*v+1] += lz[v];
      //     lz[v] = 0;
      // }
  
      // static void update(int v, int tl, int tr, int l, int r, int val) {
      //     push(v,tl,tr);
      //     if(tl>r||tr<l)
      //         return;
      //     if(tl>=l&&tr<=r){
      //         min[v] += val;
      //         lz[v] += val;
      //         return;
      //     }
      //     int tm = (tl + tr) / 2;
      //     update(v*2, tl, tm, l, r, val);
      //     update(v*2+1, tm+1, tr, l, r, val);
      //     min[v] = Math.min(min[2*v],min[2*v+1]);
      // }
  
      // static long get(int v, int tl, int tr, int l, int r) {
      //     if (tl >= l && tr <= r) {
      //         return gcd[v];
      //     }
      //     int tm = (tl + tr) / 2;
      //     if(l>tm){
      //         return get(2*v+1, tm+1, tr, l, r);
      //     }
      //     if(r<tm+1){
      //         return get(2*v, tl, tm, l, r);
      //     }
      //     return gcd(get(2*v, tl, tm, l, r), get(2*v+1, tm+1, tr, l, r));
      // }
  
      // static int y = 0;
  
      static int parent[];
      static int rank[];
  
      static int find_set(int v) {
          if (v == parent[v])
              return v;
          return find_set(parent[v]);
      }
      
      static void make_set(int v) {
          parent[v] = v;
          rank[v] = 0;
      }
      
      static void union_sets(int a, int b) {
          a = find_set(a);
          b = find_set(b);
          if (a != b) {
              if (rank[a] < rank[b]){
                  int tmp = a;
                  a = b;
                  b = tmp;
              }
              parent[b] = a;
              if (rank[a] == rank[b])
                  rank[a]++;
          }
      }
  
      static int parent1[];
      static int rank1[];
  
      static int find_set1(int v) {
          if (v == parent1[v])
              return v;
          return find_set1(parent1[v]);
      }
      
      static void make_set1(int v) {
          parent1[v] = v;
          rank1[v] = 0;
      }
      
      static void union_sets1(int a, int b) {
          a = find_set1(a);
          b = find_set1(b);
          if (a != b) {
              if (rank1[a] < rank1[b]){
                  int tmp = a;
                  a = b;
                  b = tmp;
              }
              parent1[b] = a;
              if (rank1[a] == rank1[b])
                  rank1[a]++;
          }
      }
  
      public static void solve(InputReader sc, PrintWriter pw){
          int i, j = 0;
          // int t = 1; 
          long mod = 1000000007;
          int t = sc.nextInt();
          u: while (t-- > 0) {
              int n = sc.nextInt();
              Pair k[] = new Pair[n];
              for(i=0;i<n;i++){
                  int m = sc.nextInt();
                  int y = 0;
                  for(j=0;j<m;j++){
                      y = Math.max(y,sc.nextInt()+1-j);
                  }
                  k[i] = new Pair(y,m);
              }
              Arrays.sort(k);
              int max = 0;
              int sum = 0;
              for(i=0;i<n;i++){
                  int y = k[i].a;
                  y -= sum;
                  max = Math.max(y,max);
                  sum += k[i].b;
              }
              pw.println(max);
          }
      }
  
  
      static void KMPSearch(char pat[], char txt[], int pres[])
      {
          int M = pat.length;
          int N = txt.length;
          int lps[] = new int[M];
          int j = 0; 
          computeLPSArray(pat, M, lps);
          int i = 0;
          while (i < N) {
              if (pat[j] == txt[i]) {
                  j++;
                  i++;
              }
              if (j == M) {
                  pres[i-1] = 1;
                  j = lps[j - 1];
              }
              else if (i < N && pat[j] != txt[i]) {
                  if (j != 0)
                      j = lps[j - 1];
                  else
                      i = i + 1;
              }
          }
      }
    
      static void computeLPSArray(char pat[], int M, int lps[])
      {
          int len = 0;
          int i = 1;
          lps[0] = 0; 
          while (i < M) {
              if (pat[i] == pat[len]) {
                  len++;
                  lps[i] = len;
                  i++;
              }
              else 
              {
                  if (len != 0) {
                      len = lps[len - 1];
                  }
                  else
                  {
                      lps[i] = len;
                      i++;
                  }
              }
          }
      }
  
      static long[][] matrixMult(long a[][], long b[][], long mod){
          int n = a.length;
          int m = a[0].length;
          int p = b[0].length;
          long c[][] = new long[n][p];
          for(int i=0;i<n;i++){
              for(int j=0;j<m;j++){
                  for(int k=0;k<p;k++){
                      c[i][k] += a[i][j]*b[j][k];
                      c[i][k] %= mod;
                  }
              }
          }
          return c;
      }
  
      static long[][] exp(long mat[][], long b, long mod){
          if(b==0){
              int n = mat.length;
              long res[][] = new long[n][n];
              for(int i=0;i<n;i++){
                  res[i][i] = 1;
              }
              return res;
          }
          long half[][] = exp(mat, b/2, mod);
          long res[][] = matrixMult(half, half, mod);
          if(b%2==1){
              res = matrixMult(res, mat, mod);
          }
          return res;
      }
  
      static void countPrimeFactors(int num, int a[], HashMap<Integer,Integer> pos){
          for(int i=2;i*i<num;i++){
              if(num%i==0){
                  int y = pos.get(i);
                  while(num%i==0){
                      a[y]++;
                      num/=i;
                  }
              }
          }
          if(num>1){
              int y = pos.get(num);
              a[y]++;
          }
      }
  
      static void assignAnc(ArrayList<Integer> ar[], int depth[], int sz[], int par[][] ,int curr, int parent, int d){
          depth[curr] = d;
          sz[curr] = 1;
          par[curr][0] = parent;
          for(int v:ar[curr]){
              if(parent==v)
                  continue;
              assignAnc(ar, depth, sz, par, v, curr, d+1);
              sz[curr] += sz[v];
          }
      }
  
      static int findLCA(int a, int b, int par[][], int depth[]){
          if(depth[a]>depth[b]){
              a = a^b;
              b = a^b;
              a = a^b;
          }
          int diff = depth[b] - depth[a];
          for(int i=19;i>=0;i--){
              if((diff&(1<<i))>0){
                  b = par[b][i];
              }
          }
          if(a==b)
              return a;
          for(int i=19;i>=0;i--){
              if(par[b][i]!=par[a][i]){
                  b = par[b][i];
                  a = par[a][i];
              }
          }
          return par[a][0];
      }
  
      static void formArrayForBinaryLifting(int n, int par[][]){
          for(int j=1;j<20;j++){
              for(int i=0;i<n;i++){
                  if(par[i][j-1]==-1)
                      continue;
                  par[i][j] = par[par[i][j-1]][j-1];
              }
          }
      }
  
      static long lcm(int a, int b){
          return a*b/gcd(a,b);
      }
  
      static class Pair1 {
          long a;
          long b;
          
          Pair1(long a, long b) {
              this.a = a;
              this.b = b;
          }
      }
  
      static class Pair implements Comparable<Pair> {
          int a;
          int b;
          // int c;
          
          Pair(int a, int b) {
              this.a = a;
              this.b = b;
              // this.c = c;
          }
   
          public int compareTo(Pair p) {
              // if(c!=p.c)
              return a-p.a;
              // return b-p.b;
          }
      }
  
      static class Pair2 implements Comparable<Pair2> {
          int a;
          int b;
          int c;
          
          Pair2(int a, int b, int c) {
              this.a = a;
              this.b = b;
              this.c = c;
          }
   
          public int compareTo(Pair2 p) {
              return a-p.a;
          }
      }
  
      static boolean isPrime(int n) { 
          if (n <= 1) 
              return false; 
          if (n <= 3) 
              return true; 
          if (n % 2 == 0 ||  n % 3 == 0) 
              return false; 
          for (int i = 5; i * i <= n; i = i + 6) 
              if (n % i == 0 || n % (i + 2) == 0) 
                  return false; 
          return true; 
      } 
  
      static long gcd(long a, long b) {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      static long fast_pow(long base, long n, long M) {
          if (n == 0)
              return 1;
          if (n == 1)
              return base % M;
          long halfn = fast_pow(base, n / 2, M);
          if (n % 2 == 0)
              return (halfn * halfn) % M;
          else
              return (((halfn * halfn) % M) * base) % M;
      }
  
      static long modInverse(long n, long M) {
          return fast_pow(n, M - 2, M);
      }
  
      static class InputReader {
          public BufferedReader reader;
          public StringTokenizer tokenizer;
  
          public InputReader(InputStream stream) {
              reader = new BufferedReader(new InputStreamReader(stream), 9992768);
              tokenizer = null;
          }
  
          public String next() {
              while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
      }
  }