#include <cstdio>#include <cstring>#include <vector>using namespace std;const int MAX=105;class Disjoint_Set{public:int father[MAX]; int rank[MAX]; void Init (int n){for (int i=0;i<=n;i++)Make_Set (i);}void Make_Set (int x){father[x]=x;rank[x]=1;}int Find_Set (int x){if (x != father[x])father[x] = Find_Set(father[x]);return father[x];}bool Union (int x,int y){int a=Find_Set (x);int b=Find_Set (y);if (a == b)return false;if (rank[a] >= rank[b]){father[b]=a;rank[a]+=rank[b];}else{father[a]=b;rank[b]+=rank[a];}return true;}}ob;vector<int> graphs[MAX];int predeg[MAX]; int degree[MAX];int n,m;bool Deal (){ int i; for (i=1;i<=n;i++) if (predeg[i]==1) for (int j=0;j<graphs[i].size();j++) degree[graphs[i][j]]--; int cnt=0; for (i=1;i<=n;i++) if (predeg[i]>1 && degree[i]==1) cnt++; if (cnt>2) return false; return true;}int main (){int Cas=1;while (~scanf("%d%d",&n,&m),n) {ob.Init(MAX);memset(predeg,0,sizeof(predeg));memset(degree,0,sizeof(degree));int cnt=0;bool flag=true;if (n!=m+1) flag=false; for (int i=0;i<m;i++){ int a,b; scanf("%d%d",&a,&b); predeg[a]++,degree[a]++; predeg[b]++,degree[b]++; graphs[a].push_back(b); graphs[b].push_back(a); if (ob.Union(a,b)==false) flag=false; }if (flag) { if (Deal ()) printf("Graph %d is a caterpillar.n",Cas++); else printf("Graph %d is not a caterpillar.n",Cas++); } else printf("Graph %d is not a caterpillar.n",Cas++);}return 0;}