#include<bits/stdc++.h> #define ull unsigned long long using namespace std; const int N=2e5+10,mod=1e9+9; vector<int> E[N]; int f[N],g[N],h[N],tmp[N],par[N],rng[N],siz[N],du[N]; int n; mt19937_64 rd(9517); int qp(int a,int b){ int x=1; while(b){ if(b&1) x=1ll*x*a%mod; a=1ll*a*a%mod;b>>=1; }return x; } multiset<int> H[N]; int bk(int x){ return *(--H[x].end()); } void dfs(int u,int fa){ siz[u]=1;f[u]=1;par[u]=fa; H[u].insert(1); for(auto v:E[u]){ if(v==fa) continue; dfs(v,u); siz[u]+=siz[v]; f[u]=1ll*f[u]*(f[v]+1)%mod; H[u].insert(bk(v)+1); }f[u]=1ll*f[u]*rng[bk(u)]%mod; tmp[u]=f[u]; //cout<<u<<' '<<f[u]<<endl; }//get tree hash void rev(int x){ f[x]=1ll*f[x]*qp(rng[bk(x)],mod-2)%mod; } void dfs2(int u,int fa){ if(u==1) rev(1),h[u]=1,g[u]=0; h[u]=1ll*h[u]*f[u]%mod; h[u]=1ll*rng[bk(u)]*h[u]%mod; for(auto v:E[u]){ if(v==fa) continue; g[v]=1ll*(g[u]+1)*f[u]%mod; g[v]=1ll*g[v]*qp(f[v]+1,mod-2)%mod; //cout<<v<<' '<<f[u]<<' '<<f[v]<<' '<<g[v]<<endl; //cout<<"H:"<<v<<' '<<g[v]<<endl; rev(v); int val=bk(v)+1; H[u].erase(H[u].find(val)); g[v]=1ll*g[v]*rng[bk(u)]%mod; //cout<<v<<' '<<bk(u)<<' '<<g[v]<<endl; h[v]=g[v]+1; H[v].insert(bk(u)+1); H[u].insert(val); dfs2(v,u); } } int main(){ cin>>n; for(int i=1;i<=n;i++) rng[i]=rd()%mod; for(int i=1;i<n;i++){ int u,v;cin>>u>>v; E[u].push_back(v); E[v].push_back(u); du[u]++;du[v]++; }dfs(1,0);dfs2(1,0); map<int,int> mp1; map<pair<int,int>,int> mp2; for(int i=1;i<=n;i++){ f[i]=tmp[i]; //cout<<i<<' '<<f[i]<<' '<<g[i]<<' '<<h[i]<<endl; if(du[i]<4) mp1[h[i]]=1; if(!par[i]) continue; mp2[make_pair(f[i],g[i])]=1; mp2[make_pair(g[i],f[i])]=1; }cout<<mp1.size()<<' '<<mp1.size()+mp2.size()<<endl; return 0; }