#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class a, class b> ostream& operator<<(ostream &l, const pair<a, b> &r) {
l << "(" << r.first << ", " << r.second << ")";
return l;
}
template <class t> ostream& operator<<(ostream &l, const vector<t> &r) {
l << "{";
for (int i = 0; i + 1 < r.size(); i++) l << r[i] << ", ";
if (!r.empty()) l << r.back();
l << "}";
return l;
}
template <class t> void comb(pair<t, t> &l, const pair<t, t> &r) {
// cout << "comb " << l.first << " " << l.second << " " << r.first << " " << r.second << endl;
if (r.second == 0) return;
if (l.first == r.first) l.second += r.second;
else if (l.first < r.first) l = r;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin >> n;
vector<vector<int>> adj(n);
for (int i = 1; i < n; i++) {
int a, b;
cin >> a >> b;
a--, b--;
adj[a].push_back(b);
adj[b].push_back(a);
}
vector<vector<pair<int, int>>> depths(n);
auto dfs = [&](int v, int p, auto &&self) -> pair<int, int> {
pair<int, int> cur{0, 1};
for (int i : adj[v]) {
if (i != p) {
pair<int, int> ts = self(i, v, self);
ts.first++;
depths[v].push_back(ts);
comb(cur, ts);
}
}
return cur;
};
dfs(0, -1, dfs);
vector<pair<int, int>> pd(n, {0, 1});
auto dfs1 = [&](int v, int p, auto &&self) -> void {
map<int, int> freq;
for (pair<int, int> &i : depths[v]) {
freq[i.first] += i.second;
}
int ptr = 0;
for (int i : adj[v]) {
if (i != p) {
pair<int, int> d = depths[v][ptr];
int rem = (freq[d.first] -= d.second);
if (rem == 0) freq.erase(d.first);
pd[i] = pd[v];
if (!freq.empty()) {
reverse_iterator<map<int, int>::iterator> it = freq.rbegin();
comb(pd[i], { it->first, it->second });
}
pd[i].first++;
freq[d.first] += d.second;
ptr++;
}
}
for (int i : adj[v]) {
if (i != p) {
self(i, v, self);
}
}
};
dfs1(0, -1, dfs1);
// cout << pd << endl;
pair<ll, ll> ans{0, 1};
for (int i = 0; i < n; i++) {
vector<pair<int, int>> &depth = depths[i];
if (i != 0) {
depth.push_back(pd[i]);
}
sort(depth.rbegin(), depth.rend());
// cout << "-------------" << i << " " << depths.size() << endl;
if (depth.size() > 2) {
// 0 and 1 as paths
comb(ans, {ll(depth[0].first + depth[1].first) * depth[2].first, ll(depth[0].second * depth[1].second)});
pair<int, int> pref = depth[1];
for (int j = 2; j < depth.size(); j++) {
// 0 and j as paths(padding doesn't change anything here, it's fine if depth[2].first = 0)
comb(ans, {ll(depth[0].first + depth[2].first) * depth[1].first, ll(depth[0].second) * depth[2].second});
// 0 is farthest, i < j as paths
comb(ans, {ll(depth[j].first + pref.first) * depth[0].first, ll(pref.second) * depth[j].second });
comb(pref, depth[j]);
}
}
// cout << "-------------" << i << " " << depths << endl;
//
}
cout << ans.first << " " << ans.second << '\n';
}
