A family hierarchy is usually presented by a pedigree tree where all the nodes on the same level belong to the same generation. Your task is to find the generation with the largest population.

Input Specification:

Each input file contains one test case. Each case starts with two positive integers N (<100) which is the total number of family members in the tree (and hence assume that all the members are numbered from 01 to N), and M (<N) which is the number of family members who have children. Then M lines follow, each contains the information of a family member in the following format:

ID K ID[1] ID[2] ... ID[K]

where ID is a two-digit number representing a family member, K (>0) is the number of his/her children, followed by a sequence of two-digit ID's of his/her children. For the sake of simplicity, let us fix the root ID to be 01. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in one line the largest population number and the level of the corresponding generation. It is assumed that such a generation is unique, and the root level is defined to be 1.

Sample Input:

23 13

21 1 23

01 4 03 02 04 05

03 3 06 07 08

06 2 12 13

13 1 21

08 2 15 16

02 2 09 10

11 2 19 20

17 1 22

05 1 11

07 1 14

09 1 17

10 1 18

Sample Output:

9 4

 #include<string>

 #include<iostream>

 #include<map>

 #include<stdio.h>

 #include<vector>

 using namespace std;

 struct node

 {

     vector<int> child;

 };

 node Tree[];

 int Level[];

 int MAX = -;

 void DFS(int n,int level)

 {

     if(MAX < level)

         MAX = level;

     ++Level[level];

     for(int i =  ;i < Tree[n].child.size() ;++i)

         DFS(Tree[n].child[i],level+);

 }

 int main()

 {

     int n,m,tid,num,id;

     scanf("%d%d",&n,&m);

     for(int i =  ;i < m ;++i)

     {

         scanf("%d%d",&id,&num);

         for(int k = ;k < num;++k)

         {

             scanf("%d",&tid);

             Tree[id].child.push_back(tid);

         }

     }

     DFS(,);

     int maxL = -;

     int index = -;

     for(int i = ; i <= MAX;++i)

     {

         if(Level[i] > maxL)

         {

             maxL = Level[i];

             index = i;

         }

     }

     printf("%d %d\n",maxL,index);

     return ;

 }