#include <iostream>
#include <vector>
#include <cstring>
#include <string>
#include <iomanip>
#include <algorithm>
#include <fstream>
#include <cmath>
#include <unordered_set>
#include <set>
#include <unordered_map>
#include <map>
#define ll long long
#define X first
#define Y second
#define endl '\n'
using namespace std;
void speed()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
}
const int MAXN = 500010;
int n;
vector<int> v[MAXN];
pair<int, ll> dp1[MAXN];
pair<int, ll> dp2[MAXN];
void mert(pair<int, ll> &x, pair<int, ll> y)
{
if (x.X > y.X)
return;
if (x.X < y.X)
{
x = y;
return;
}
x.Y += y.Y;
}
void read()
{
cin >> n;
for (int i = 1; i < n; i++)
{
int x, y;
cin >> x >> y;
v[x].push_back(y);
v[y].push_back(x);
}
}
pair<int, ll> operator+(pair<int, ll> x, int val)
{
return {x.X + val, x.Y};
}
void dfs1(int beg, int par)
{
bool l=0;
for (int nb : v[beg])
{
if (nb == par)
continue;
dfs1(nb, beg);
l=1;
mert(dp1[beg], dp1[nb] + 1);
}
if (v[beg].size())
mert(dp1[beg] , {0, 1});
}
int parr[MAXN];
void dfs2(int beg, int par)
{
parr[beg] = par;
vector<int> kids;
for (int nb : v[beg])
{
if (nb == par)
continue;
kids.push_back(nb);
}
if (kids.empty())
return;
int sz = kids.size();
vector<pair<int, ll>> pref(sz), sufx(sz);
pref[0] = dp1[kids[0]] + 1;
for (int i = 1; i < sz; i++)
{
pref[i] = pref[i - 1];
mert(pref[i], dp1[kids[i]] + 1);
}
sufx.back() = dp1[kids.back()] + 1;
for (int i = sz - 2; i >= 0; i--)
{
sufx[i] = sufx[i + 1];
mert(sufx[i], dp1[kids[i]] + 1);
}
for (int i = 0; i < sz; i++)
{
pair<int, ll> val = dp2[beg];
if (i - 1 >= 0)
mert(val, pref[i - 1]);
if (i + 1 < sz)
mert(val, sufx[i + 1]);
int nb = kids[i];
dp2[nb] = val + 1;
dfs2(nb, beg);
}
}
vector<pair<int, ll>> ex(int x)
{
vector<pair<int, ll>> ans;
if (dp2[x].Y > 0)
ans.push_back(dp2[x]);
for (int nb : v[x])
{
if (nb == parr[x])
continue;
ans.push_back(dp1[nb] + 1);
}
sort(ans.begin(), ans.end(), [](auto &a, auto &b)
{ return a.X > b.X; });
return ans;
}
signed main()
{
speed();
read();
dp2[1] = {0, 0};
dfs1(1, 0);
dfs2(1, 0);
ll ba = -1;
for (int i = 1; i <= n; i++)
{
vector<pair<int, ll>> v = ex(i);
if (v.size() < 3)
continue;
ba = max(ba, (ll)(v[0].X * (v[1].X + v[2].X)));
}
if (ba == -1)
{
cout << 0 << " " << 1 << endl;
return 0;
}
ll cnt = 0;
for (int i = 1; i <= n; i++)
{
vector<pair<int, ll>> v = ex(i);
if (v.size() < 3)
continue;
if (v[0].X * (v[1].X + v[2].X) != ba)
continue;
int a = v[0].X;
int b = v[1].X;
int c = v[2].X;
if (a == b && b == c)
{
ll sum1 = 0, sum2 = 0;
ll ans = 0;
for (int i = 0; i < v.size(); i++)
{
if (v[i].X != v[0].X)
break;
sum1 += v[i].Y;
sum2 += v[i].Y * v[i].Y;
}
ans = sum1 * sum1 - sum2;
ans /= 2;
cnt += ans;
}
else if (a != b && b == c)
{
ll sum1 = 0, sum2 = 0;
ll ans = 0;
for (int i = 1; i < v.size(); i++)
{
if (v[i].X != v[1].X)
break;
sum1 += v[i].Y;
sum2 += v[i].Y * v[i].Y;
}
ans = sum1 * sum1 - sum2;
ans /= 2;
cnt += ans;
}
else if (a == b && b != c)
{
ll sum = 0;
for (int i = 2; i < v.size(); i++)
{
if (v[i].X != v[2].X)
break;
sum += v[i].Y;
}
cnt += sum * (v[0].Y + v[1].Y);
}
else
{
ll sum = 0;
for (int i = 2; i < v.size(); i++)
{
if (v[i].X != v[2].X)
break;
sum += v[i].Y;
}
cnt += sum * (v[1].Y);
}
}
cout << ba << ' ' << cnt << endl;
return 0;
}
