#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'; }