#include <bits/stdc++.h>
#define ll long long
#define MAXN 500010
using namespace std;
ll maxx[MAXN],cnt[MAXN];
vector<ll> G[MAXN];
void DFS_Dist(ll i,ll p)
{
maxx[i]=0;
cnt[i]=1;
for (ll next : G[i])
{
if (next!=p)
{
DFS_Dist(next,i);
if (maxx[next]+1==maxx[i])
cnt[i]+=cnt[next];
else if (maxx[next]+1>maxx[i])
{
maxx[i]=maxx[next]+1;
cnt[i]=cnt[next];
}
}
}
}
vector<pair<ll,ll> > dist[MAXN];
ll ans,cntans=1;
void DFS_Solve(ll i,ll p)
{
if (p)
{
if (dist[p][0].first==maxx[i]+1 && dist[p][0].second==cnt[i])
{
if (dist[p].size()>1)
dist[i].push_back({dist[p][1].first+1,dist[p][1].second});
else
dist[i].push_back({1,1});
}
else
dist[i].push_back({dist[p][0].first+1,dist[p][0].second});
}
for (ll next : G[i])
{
if (next!=p)
dist[i].push_back({maxx[next]+1,cnt[next]});
}
sort(dist[i].begin(),dist[i].end(),greater<pair<ll,ll> >());
ll maxxh=0,cur=0;
if (dist[i].size()>2)
{
ll maxx1=dist[i][0].first,maxx2=dist[i][1].first,maxx3=dist[i][2].first,same=0;
maxxh=maxx1*(maxx2+maxx3);
for (auto i : dist[i])
{
if (i.first==maxx3)
same+=i.second;
}
if (maxx1!=maxx2 && maxx2!=maxx3)
cur+=dist[i][1].second*same;
else if (maxx1==maxx2 && maxx2!=maxx3)
cur+=(dist[i][0].second+dist[i][1].second)*same;
else
{
for (auto i : dist[i])
{
if (i.first==maxx3)
cur+=i.second*(same-i.second);
}
cur/=2;
}
if (maxxh>ans && cur)
{
ans=maxxh;
cntans=cur;
}
else if (maxxh==ans)
cntans+=cur;
}
for (ll next : G[i])
{
if (next!=p)
DFS_Solve(next,i);
}
}
int main()
{
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
ll n,u,v;
cin >> n;
for (ll i=1;i<n;i++)
{
cin >> u >> v;
G[u].push_back(v);
G[v].push_back(u);
}
DFS_Dist(1,0);
DFS_Solve(1,0);
cout << ans << " " << cntans << "\n";
return 0;
}
