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.util.*;
  import java.io.*;
  // import java.lang.*;
  // import java.math.*;
  
  public class Codeforces {
      static FastReader sc=new FastReader();
  	static PrintWriter out=new PrintWriter(System.out);
  	static long mod=1000000007;
  	// static long mod=998244353;
  	static int MAX=Integer.MAX_VALUE;
  	static int MIN=Integer.MIN_VALUE;
  	static long MAXL=Long.MAX_VALUE;
  	static long MINL=Long.MIN_VALUE;
  	static ArrayList<Integer> graph[];
  	public static void main (String[] args) throws java.lang.Exception
  	{
  		// code goes here
  		int t=I();
  		while(t-->0)
  		{
  			int n=I();
  			ArrayList<pair> arr=new ArrayList<>();
  			for(int i=0;i<n;i++){
  				int len=I();
  				long sum=0;
  				long a[]=new long[len];
  				a[0]=L();
  				sum=a[0]+1;
  				long zsum=sum+1;
  				for(int j=1;j<len;j++){
  					a[j]=L();
  					if(a[j]<zsum){
  						zsum++;
  					}else{
  						sum=a[j]+1-j;
  						zsum=sum+j+1;
  					}
  				}
  				arr.add(new pair(sum,len));
  			}
  			Collections.sort(arr,new myComp());
  			// for(pair p:arr){
  			// 	out.println(p.a+"->"+p.b);
  			// }
  			long ans=arr.get(0).a;
  			// long prev=arr.get(0).a;
  			long esum=arr.get(0).a+arr.get(0).b;
  			for(int i=1;i<arr.size();i++){
  				if(esum<arr.get(i).a){
  					ans=ans+(arr.get(i).a-esum);
  					esum+=arr.get(i).a-esum;
  					esum+=arr.get(i).b;
  					// esum+=arr.get(i).a+arr.get(i).b-prev;
  					// prev=arr.get(i).a;
  				}else{
  					esum+=arr.get(i).b;
  				}
  				// out.println(esum+" "+ans);
  			}
  			out.println(ans);
  		}
  		out.close();
  	}
  	public static class pair
      {
      	long a;
      	long b;
      	public pair(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
  	public static class myComp implements Comparator<pair>
  	{
  		//sort in ascending order.
  		public int compare(pair p1,pair p2)
  		{
  			if(p1.a==p2.a)
      	    return 0;
      	    else if(p1.a<p2.a)
      	    return -1;
      	    else
      	    return 1;
  		}
  		//sort in descending order.
  		// public int compare(pair p1,pair p2)
      	// {
      	//     if(p1.a==p2.a)
      	//     return 0;
      	//     else if(p1.a<p2.a)
      	//     return 1;
      	//     else
      	//     return -1;
      	// }
  	}
  	public static long kadane(long a[],int n)
  	{
  		long max_sum=Long.MIN_VALUE,max_end=0;
  		for(int i=0;i<n;i++){
  			max_end+=a[i];
  			if(max_sum<max_end){max_sum=max_end;}
  			if(max_end<0){max_end=0;}
  		}
  		return max_sum;
  	}
  	public static void DFS(int s,boolean visited[])
  	{
  		visited[s]=true;
  		for(int i:graph[s]){
  			if(!visited[i]){
  				DFS(i,visited);
  			}
  		}
  	}
  	public static void setGraph(int n,int m)
  	{
  		graph=new ArrayList[n+1];
  		for(int i=0;i<=n;i++){
  			graph[i]=new ArrayList<>();
  		}
  		for(int i=0;i<m;i++){
  			int u=I(),v=I();
  			graph[u].add(v);
  			graph[v].add(u);
  		}
  	}
  	public static int BS(long a[],long x,int ii,int jj)
  	{
  		// int n=a.length;
  		int mid=0;
  		int i=ii,j=jj;
  		while(i<=j)
  		{
  			mid=(i+j)/2;
  			if(a[mid]<x){
  				i=mid+1;
  			}else if(a[mid]>x){
  				j=mid-1;
  			}else{
  				return mid;
  			}
  		}
  		return -1;
  	}
  	public static int lower_bound(int arr[],int s, int N, int X)
  	{
  		if(arr[N]<X)return N;
  		if(arr[0]>X)return -1;
  		int left=s,right=N;
  		while(left<right){
  			int mid=(left+right)/2;
  			if(arr[mid]==X)
  			return mid;
  			else if(arr[mid]>X){
  				if(mid>0 && arr[mid]>X && arr[mid-1]<=X){
  					return mid-1;
  				}else{
  					right=mid-1;
  				}
  			}else{
  				if(mid<N && arr[mid+1]>X && arr[mid]<=X){
  					return mid;
  				}else{
  					left=mid+1;
  				}
  			}
  		}
  		return left;
  	}
  	public static ArrayList<Integer> primeSieve(int n)
  	{
  	    ArrayList<Integer> arr=new ArrayList<>();
  	    boolean prime[] = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
          prime[i] = true;
          for (int p = 2; p * p <= n; p++)
          {
              if (prime[p] == true)
              {
                  for (int i = p * p; i <= n; i += p)
                  prime[i] = false;
              }
          }
          for (int i = 2; i <= n; i++)
          {
              if (prime[i] == true)
              arr.add(i);
          }
          return arr;
  	}
  
  	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
  	public static class FenwickTree
  	{
  		int farr[];
  		int n;
  		public FenwickTree(int c)
  		{
  			n=c+1;
  			farr=new int[n];
  		}
  		// public void update_range(int l,int r,long p)
  		// {
  		// 	update(l,p);
  		// 	update(r+1,(-1)*p);
  		// }
  		public void update(int x,int p)
  		{
  			for(;x<=n;x+=x&(-x))
  			{
  				farr[x]+=p;
  			}
  		}
  		public long get(int x)
  		{
  			long ans=0;
  			for(;x>0;x-=x&(-x))
  			{
  				ans=ans+farr[x];
  			}
  			return ans;
  		}
  	}
  
  	//Disjoint Set Union
  	public static class DSU
  	{
  	    int par[],rank[];
  	    public DSU(int c)
  	    {
  	        par=new int[c+1];
  	        rank=new int[c+1];
  	        for(int i=0;i<=c;i++)
  	        {
  	            par[i]=i;
  	            rank[i]=0;
  	        }
  	    }
  	    public int find(int a)
  	    {
  	        if(a==par[a])
  	        return a;
  	        return par[a]=find(par[a]);
  	    }
  	    public void union(int a,int b)
  	    {
  	        int a_rep=find(a),b_rep=find(b);
  	        if(a_rep==b_rep)
  	        return;
  	        if(rank[a_rep]<rank[b_rep])
  	        par[a_rep]=b_rep;
  	        else if(rank[a_rep]>rank[b_rep])
  	        par[b_rep]=a_rep;
  	        else
  	        {
  	            par[b_rep]=a_rep;
  	            rank[a_rep]++;
  	        }
  	    }
  	}
  
  	//SEGMENT TREE CODE
  
  	// public static void segmentUpdate(int si,int ss,int se,int qs,int qe,long x)
  	// {
  	// 	if(ss>qe || se<qs)return;
  	// 	if(qs<=ss && qe>=se)
  	// 	{
  	// 		seg[si][0]+=1L;
  	// 		seg[si][1]+=x*x;
  	// 		seg[si][2]+=2*x;
  	// 		return;
  	// 	}
  	// 	int mid=(ss+se)/2;
  	// 	segmentUpdate(2*si+1,ss,mid,qs,qe,x);
  	// 	segmentUpdate(2*si+2,mid+1,se,qs,qe,x);
  	// }
  	// public static long segmentGet(int si,int ss,int se,int x,long f,long s,long t,long a[])
  	// {
  	// 	if(ss==se && ss==x)
  	// 	{
  	// 		f+=seg[si][0];
  	// 		s+=seg[si][1];
  	// 		t+=seg[si][2];
  	// 		long ans=a[x]+(f*((long)x+1L)*((long)x+1L))+s+(t*((long)x+1L));
  	// 		return ans;
  	// 	}
  	// 	int mid=(ss+se)/2;
  	// 	if(x>mid){
  	// 		return segmentGet(2*si+2,mid+1,se,x,f+seg[si][0],s+seg[si][1],t+seg[si][2],a);
  	// 	}else{
  	// 		return segmentGet(2*si+1,ss,mid,x,f+seg[si][0],s+seg[si][1],t+seg[si][2],a);
  	// 	}
  	// }
  
  	
      public static class myComp1 implements Comparator<pair1>
      {
  		//sort in ascending order.
      	public int compare(pair1 p1,pair1 p2)
      	{
      	    if(p1.a==p2.a)
      	    return 0;
      	    else if(p1.a<p2.a)
      	    return -1;
      	    else
      	    return 1;
      	}
  		//sort in descending order.
  		// public int compare(pair p1,pair p2)
      	// {
      	//     if(p1.a==p2.a)
      	//     return 0;
      	//     else if(p1.a<p2.a)
      	//     return 1;
      	//     else
      	//     return -1;
      	// }
      }
  	public static class pair1
      {
      	long a;
      	long b;
      	public pair1(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
      public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
  	{
  	    //****************use this in main function-Collections.sort(arr,new myComp1());
  	    ArrayList<pair1> a1=new ArrayList<>();
  	    if(arr.size()<=1)
  	    return arr;
  	    a1.add(arr.get(0));
  	    int i=1,j=0;
  	    while(i<arr.size())
  	    {
  	        if(a1.get(j).b<arr.get(i).a)
  	        {
  	           a1.add(arr.get(i));
  	           i++;
  	           j++;
  	        }
  	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
  	        {
  	            i++;
  	        }
  	        else if(a1.get(j).b>=arr.get(i).a)
  	        {
  	            long a=a1.get(j).a;
  	            long b=arr.get(i).b;
  	            a1.remove(j);
  	            a1.add(new pair1(a,b));
  	            i++;
  	        }
  	    }
  	    return a1;
  	}
  	public static boolean isPalindrome(String s,int n)
  	{
  		for(int i=0;i<=n/2;i++){
  			if(s.charAt(i)!=s.charAt(n-i-1)){
  				return false;
  			}
  		}
  		return true;
  	}
  	public static int gcd(int a,int b)
  	{
  	    if(b==0)
  	    return a;
  	    else
  	    return gcd(b,a%b);
  	}
  	public static long gcd(long a,long b)
  	{
  	    if(b==0)
  	    return a;
  	    else
  	    return gcd(b,a%b);
  	}
  	public static long fact(long n)
  	{
  		long fact=1;
  		for(long i=2;i<=n;i++){
  			fact=((fact%mod)*(i%mod))%mod;
  		}
  		return fact;
  	}
  	public static long fact(int n)
  	{
  		long fact=1;
  		for(int i=2;i<=n;i++){
  			fact=((fact%mod)*(i%mod))%mod;
  		}
  		return fact;
  	} 
  	public static boolean isPrime(int n) 
  	{ 
  	    if (n <= 1) 
  	        return false; 
  	    if (n <= 3) 
  	        return true; 
  	    if (n % 2 == 0 || n % 3 == 0) 
  	        return false; 
  	    double sq=Math.sqrt(n);
  	  
  	    for (int i = 5; i <= sq; i = i + 6) 
  	        if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	    return true; 
  	} 
      public static boolean isPrime(long n) 
  	{ 
  	    if (n <= 1) 
  	        return false; 
  	    if (n <= 3) 
  	        return true; 
  	    if (n % 2 == 0 || n % 3 == 0) 
  	        return false; 
  	    double sq=Math.sqrt(n);
  	
  	    for (int i = 5; i <= sq; i = i + 6) 
  	        if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	    return true; 
  	}
  	public static void printArray(long a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(int a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(pair a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i].a+"->"+a[i].b+" ");
  		}
  		out.println();
  	}
  	public static void printArray(char a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]);
  		}
  		out.println();
  	}
  	public static void printArray(String a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(boolean a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(int a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArray(long a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArray(char a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArrayL(ArrayList<Long> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printArrayI(ArrayList<Integer> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printArrayS(ArrayList<String> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printMapInt(HashMap<Integer,Integer> hm){
  		for(Map.Entry<Integer,Integer> e:hm.entrySet()){
  			out.println(e.getKey()+"->"+e.getValue());
  		}out.println();
  	}
  	public static void printMapLong(HashMap<Long,Long> hm){
  		for(Map.Entry<Long,Long> e:hm.entrySet()){
  			out.println(e.getKey()+"->"+e.getValue());
  		}out.println();
  	}
  
  	//Modular Arithmetic
  
  	public static long add(long a,long b)
  	{
  		a+=b;
  		if(a>=mod)a-=mod;
  		return a;
  	}
  	public static long sub(long a,long b)
  	{
  		a-=b;
  		if(a<0)a+=mod;
  		return a;
  	}
  	public static long mul(long a,long b)
  	{
  		return ((a%mod)*(b%mod))%mod;
  	}
  	public static long divide(long a,long b,long m)
  	{
  		a=mul(a,modInverse(b,m));
  		return a;
  	}
  	public static long modInverse(long a,long m)
  	{
  		int x=0,y=0;
  		own p=new own(x,y);
  		long g=gcdExt(a,m,p);
  		if(g!=1){
  			out.println("inverse does not exists");
  			return -1;
  		}else{
  			long res=((p.a%m)+m)%m;
  			return res;
  		}
  	}
  	public static long gcdExt(long a,long b,own p)
  	{
  		if(b==0){
  			p.a=1;
  			p.b=0;
  			return a;
  		}
  		int x1=0,y1=0;
  		own p1=new own(x1,y1);
  		long gcd=gcdExt(b,a%b,p1);
  		p.b=p1.a - (a/b) * p1.b;
  		p.a=p1.b;
  		return gcd;
  	}
  	public static long pwr(long m,long n)
  	{
  		long res=1;
  		m=m%mod;
  		if(m==0)
  		return 0;
  		while(n>0)
  		{
  			if((n&1)!=0)
  			{
  				res=(res*m)%mod;
  			}
  			n=n>>1;
  			m=(m*m)%mod;
  		}
  		return res;
  	}
  	public static class own
      {
      	long a;
      	long b;
      	public own(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
  
  	//Modular Airthmetic
  
  	public static void sort(int[] A)
  	{
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              int tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
      }
      public static void sort(long[] A)
  	{
  	    int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              long tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
  	    Arrays.sort(A);
  	}
  	public static int I(){return sc.I();}
      public static long L(){return sc.L();}
      public static String S(){return sc.S();}
      public static double D(){return sc.D();}
  }
  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 I(){ 
          return Integer.parseInt(next());
      }
      long L(){ 
          return Long.parseLong(next());
      }
      double D(){
           return Double.parseDouble(next());
      }
      String S(){
          String str = "";
          try 
          {
              str = br.readLine();
          }
          catch (IOException e)
          {
              e.printStackTrace();
          }
          return str;
      }
  }
  