#include"bits/stdc++.h"
using namespace std;
using ll=long long;
#define S second
#define F first
const int mxn=6e5;
ll par[mxn],d[mxn],mx,x,Sigma,y,Alpha,IDontLikeSpecialCases,MaximumOfTheGalaxy[mxn],WHEREISOMNIMANWHEREISHE,AREYOUSURE,ANNOYINGFERMAT;
bool DoubleFreakyNoCap[mxn],tm8x[mxn],tm8y[mxn];
vector<ll>adj[mxn],pth,cur;
bool Freaky[mxn],f=1;
void dia(int i,int p,int l){
for(int j:adj[i]){
if(j==p)continue;
dia(j,i,l+1);
}
if(l>mx){
if(f)x=i,Sigma=1;
else y=i,Alpha=1;
mx=l;
}
else if(l==mx){
if(f)Sigma++;
else Alpha++;
}
}
void dfs(int i,int p){
cur.push_back(i);
for(int j:adj[i]){
if(j==p)continue;
dfs(j,i);
}
if(i==y)pth=cur;
cur.pop_back();
}
void FreaknessLevel(int i,int p,int l,bool t){
for(int j:adj[i]){
if(j==p)continue;
FreaknessLevel(j,i,l+1,t);
}
if(l==mx){
if(Freaky[i])DoubleFreakyNoCap[i]=1,ANNOYINGFERMAT++;
else Freaky[i]=1;
}
if(!t&&Freaky[i]&&!DoubleFreakyNoCap[i]){
if(l==mx)WHEREISOMNIMANWHEREISHE++,tm8x[i]=1;
else AREYOUSURE++,tm8y[i]=1;
}
}
void calc(int i,int p,int pre,int nxt,ll l,int ExtremeParent){
par[i]=ExtremeParent;
for(int j:adj[i]){
if(j==p||j==pre||j==nxt)continue;
calc(j,i,0,0,l+1,ExtremeParent);
}
IDontLikeSpecialCases=max(IDontLikeSpecialCases,l);
MaximumOfTheGalaxy[i]=l;
}
ll IMSOLONELY(ll a,ll b,ll c){
return a*b+c*(c-1)/2+c*(a+b);
}
int main(){
cin.tie(0)->sync_with_stdio(0);
int n;
cin>>n;
f=1;
for(int i=1,a,b;i<n;i++){
cin>>a>>b;
adj[a].push_back(b);
adj[b].push_back(a);
if(adj[a].size()>2||adj[b].size()>2)f=0;
}
if(f)return cout<<"0 1",0;
f=1,mx=0;dia(1,0,0);
f=0,mx=0;dia(x,0,0);
f=1,mx=0;dia(y,0,0);
FreaknessLevel(x,0,0,1);
FreaknessLevel(y,0,0,0);
dfs(x,0);
for(int i=0;i<=mx;i++){
calc(pth[i],0,(i?pth[i-1]:0),(i<mx?pth[i+1]:0),0,pth[i]);
d[pth[i]]=i;
}
pair<ll,ll>res={mx*IDontLikeSpecialCases,0ll};
Sigma++,Alpha++;
for(int i=1;i<=n;i++){
if((int)adj[i].size()>1||i==x||i==y)continue;
ll a=d[par[i]]*(MaximumOfTheGalaxy[i]+mx-d[par[i]]);
ll b=(mx-d[par[i]])*(MaximumOfTheGalaxy[i]+d[par[i]]);
res.F=max({res.F,a,b});
}
ll A=0,B=0,C=0;
bool fr[2]={1,1};
for(int i=1;i<=n;i++){
if((int)adj[i].size()>1||i==x||i==y)continue;
ll a=d[par[i]]*(MaximumOfTheGalaxy[i]+mx-d[par[i]]); //y
ll b=(mx-d[par[i]])*(MaximumOfTheGalaxy[i]+d[par[i]]); //x
if(max(a,b)!=res.F)continue;
if(DoubleFreakyNoCap[i]){
A=(ANNOYINGFERMAT+1)*(ANNOYINGFERMAT+2)/2ll;
B=0,C=0;
break;
}
else if(Freaky[i]){
if(tm8x[i]&&fr[0]){
B+=WHEREISOMNIMANWHEREISHE-1;
C+=ANNOYINGFERMAT;
fr[0]=0;
}
else if(tm8y[i]&&fr[1]){
B+=AREYOUSURE-1;
C+=ANNOYINGFERMAT;
fr[1]=0;
}
B+=(a>b?AREYOUSURE-1:WHEREISOMNIMANWHEREISHE-1);
C+=ANNOYINGFERMAT;
}
else{
if(a==b)C+=WHEREISOMNIMANWHEREISHE+AREYOUSURE+ANNOYINGFERMAT;
else C+=(a>b?AREYOUSURE:WHEREISOMNIMANWHEREISHE)+ANNOYINGFERMAT;
}
}
// cout<<"f";
// if(res.F==75180)cout<<A<<' '<<B<<' '<<C<<'\n';
cout<<res.F<<' '<<A+B/2ll/(fr[0]^fr[1]?2ll:1ll)+C;
// cout<<'\n'<<ANNOYINGFERMAT<<' '<<WHEREISOMNIMANWHEREISHE<<' '<<AREYOUSURE;
// cout<<'\n'<<x<<' '<<y;
// cout<<'\n'<<IMSOLONELY(WHEREISOMNIMANWHEREISHE,AREYOUSURE,ANNOYINGFERMAT-1);
}
