/*
   Prints state expansions at time t for a FSA. Starts with 1 token in state 0.


maxtime
4  5  (means and edge from 4 to 5)
3  6
-1



Generates the FSA database. 
FILENAME= nodes.edges.number
File stores:
The first 30 terms of the sequence.
-1
The FSM in edge format
//This is tested for graph isomormphism to disallow multiple entries
-1
hyperlinks to files with the same sequence

Updates MasterFile:
A list of all files sorted in "alphabetical" order of their sequences.


Traversal Algorithm:
0 0
0 1
1 0
1 1

0 0
0 1
0 2
1 0
1 1
1 2
2 0
2 1
2 2

...
Lists all posible edges.
Takes all subsets, with at least one in degree on every vertex except 0.
       -Check for connectivity
       -Check for isomorphism
           -sequence isomorphism
	   -nodes and edges isomorphism
           -permute edges to see if isomorphic
       -Adds to database if not isomorphic
*/

#include<stdio.h>
#include<gmp.h>

#define MAX_EDGES 10000
#define MAX_STATES 100


int states[MAX_STATES][MAX_EDGES];
int edges[MAX_STATES];
mpz_t SUMS[MAX_STATES];
mpz_t NEW_SUMS[MAX_STATES];
mpz_t SUM;
int maxTime;
int stateNum;

int pairs[10000][2];
int choices[10000];
int pairNum=1;
int CUR_EDGES=1;
int CUR_VERTS=1;


int dfsFindNext()
{
  int i,j,k;
  


}


getNextSequence()
{
  int i,j,k;
  if(CUR_EDGES*CUR_VERTS==pairNum)
    {
      CUR_VERTS++;
      pairNum=CUR_VERTS*CUR_VERTS;
      CUR_EDGES=CUR_VERTS-1;
      for(i=0;i<pairNum;i++)
	{
	  pairs[i][1]=i%CUR_VERTS;
	  choices[i]=0;
	}
      for(i=0;i<CUR_VERTS;i++)
	{
	  for(j=0;j<CUR_VERTS;j++)
	    pairs[i][0]=i;
	}
    }
  /*
  hmmm. 
  Algorithm to enumerate all rooted trees of order n?
  Put 1 edge everywhere...
  Put 2 edges everywhere...
  Put 4 edges everywhere...
  ...(Start out by checking to see if every vertex has an edge)
 
  -it should ignore a good chunk that it finds isomorphic

  For large n via random edge inclusion?
  */


}




int main()
{
  int i,j,k;

  for(i=0;i<MAX_STATES;i++)
    {
      mpz_init(SUMS[i]);
      mpz_init(NEW_SUMS[i]);
      mpz_set_ui(SUMS[i],0);
      edges[i]=0;
    }
  mpz_init(SUM);

  getNextSequence();



  mpz_set_ui(SUMS[0],1);


  gmp_scanf("%d",&maxTime);
  
  for(i=0;i<1000000;i++)
    {
      gmp_scanf("%d",&j);
      if(j<0)
	break;
      gmp_scanf("%d",&k);
      if(j>=stateNum)
	stateNum=j+1;
      if(k>=stateNum)
	stateNum=k+1;
      states[j][edges[j]]=k;
      edges[j]++;
    }
  gmp_printf("1\n");
  for(i=0;i<maxTime;i++)
    {
      for(j=0;j<stateNum;j++)
	  mpz_set_ui(NEW_SUMS[j],0);
      for(j=0;j<stateNum;j++)
	{
	  for(k=0;k<edges[j];k++)
	    mpz_add(NEW_SUMS[states[j][k]],
		    NEW_SUMS[states[j][k]],
		    SUMS[j]);
	}
      for(j=0;j<stateNum;j++)
	mpz_set(SUMS[j],NEW_SUMS[j]);
      
      mpz_set_ui(SUM,0);
      for(j=0;j<stateNum;j++)
	mpz_add(SUM,SUM,SUMS[j]);
      gmp_printf("%Zd\n",SUM);
       
    }


}