#include <bits/stdc++.h>
using namespace std;
#define N 300010
#define M 3
#define INF 1000000010
#define fi first
#define se second
#define pb push_back
typedef long long ll;
typedef pair< ll, ll > pll;
typedef vector< ll > vl;
typedef vector< pll > vll;
ll n;
vl grafo[N];
pll invalid = {0, 0};
pll fart[N][M+1];
pll aux[N][M+1];
pll dp[N];
void Add(ll u, ll val)
{
for(ll i = 1;i <= M;i++)
{
if(fart[u][i].fi != val) continue;
fart[u][i].se++;
return;
}
if(fart[u][M].fi < val) fart[u][M] = {val, 1LL};
sort(fart[u] + 1, fart[u] + M + 1, greater< pll >());
return;
}
void Rem(ll u, ll val)
{
for(ll i = 1;i <= M;i++)
{
if(fart[u][i].fi != val) continue;
fart[u][i].se--;
if(fart[u][i].se != 0) return;
fart[u][i] = invalid;
break;
}
sort(fart[u] + 1, fart[u] + M + 1, greater< pll >());
return;
}
void Copy(pll *a, pll *b)
{
for(ll i = 1;i <= M;i++) b[i] = a[i];
return;
}
pll Calc(pll *vet)
{
if(vet[1].se + vet[2].se + vet[3].se < 3) return invalid;
ll a, b;
if(vet[1].se >= 3)
{
a = vet[1].fi * (vet[1].fi + vet[1].fi);
b = (vet[1].se * (vet[1].se - 1)) / 2;
}else if(vet[1].se == 2)
{
a = vet[1].fi * (vet[1].fi + vet[2].fi);
b = vet[1].se * vet[2].se;
}else if(vet[2].se >= 2)
{
a = vet[1].fi * (vet[2].fi + vet[2].fi);
b = (vet[2].se * (vet[2].se - 1)) / 2;
}else
{
a = vet[1].fi * (vet[2].fi + vet[3].fi);
b = vet[2].se * vet[3].se;
}
return {a, b};
}
void DFS(ll u, ll pai)
{
for(ll i = 1;i <= M;i++) fart[u][i] = invalid;
for(auto v : grafo[u])
{
if(v == pai) continue;
DFS(v, u);
Add(u, fart[v][1].fi+1);
}
return;
}
void Solv(ll u, ll pai)
{
dp[u] = Calc(fart[u]);
Copy(fart[u], aux[u]);
for(auto v : grafo[u])
{
if(v == pai) continue;
Rem(u, fart[v][1].fi+1);
if((fart[u][1].fi != u) || (fart[u][1].se == 1))
{
Add(v, fart[u][1].fi+1);
}else
{
Add(v, fart[u][2].fi+1);
}
Solv(v, u);
Copy(aux[u], fart[u]);
}
return;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
ll u, v, i;
cin >> n;
for(i = 1;i < n;i++)
{
cin >> u >> v;
grafo[u].pb(v);
grafo[v].pb(u);
}
DFS(1, 1);
Solv(1, 1);
sort(dp + 1, dp + n + 1, greater< pll >());
dp[n+1] = {-1, -1};
i = 2;
while(dp[i].fi == dp[1].fi) dp[1].se += dp[i++].se;
if(dp[1].se == 0) dp[1].se = 1;
cout << dp[1].fi << " " << dp[1].se << endl;
return 0;
}
