// Starcraft 2 enjoyer // #include <bits/stdc++.h> // #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") using namespace std; #define LSOne(X) ((X) & -(X)) #define int long long const int N = 5e5 + 5; const int M = 1e3 + 5; const int LG = 60; const int C = 26; const long long INF = 2e9 + 5; const int B = 400; const int MOD = 1e9 + 7; int n, m; vector<int> adj[N]; long long ans, mx[N], cnt, up[N], num[N]; void dfs1(int c, int p) { for (int i : adj[c]) { if (i == p) continue; dfs1(i, c); mx[c] = max(mx[c], mx[i] + 1); } } void add(int &i, int j, int &z, int a) { if (i < j) { z = a; i = j; } else if (i == j) { z += a; } } void dfs2(int c, int p) { vector<int> v; map<int, int> mp; for (int i : adj[c]) { if (i == p) continue; mp[mx[i] + 1]++; v.push_back(mx[i] + 1); up[i] = max(up[i], up[c] + 1); num[i] = 1; } mp[up[c]] += num[c]; v.push_back(up[c]); sort(v.rbegin(), v.rend()); if (v.size() > 2) { if (ans < v[0] * (v[1] + v[2])) { ans = v[0] * (v[1] + v[2]); cnt = 0; } if (ans <= v[0] * (v[1] + v[2])) { // cout << ans << " " << cnt << "\n"; // cout << mp[v[1]] << "\n"; if (v[1] == v[2]) { cnt += mp[v[1]] * (mp[v[2]] - 1) / 2; } else { cnt += mp[v[1]] * mp[v[2]]; } // cout << ans << " " << cnt << "\n"; } } int cmx = -1, a = 0; for (int i : adj[c]) { if (i == p) continue; add(up[i], cmx + 2, num[i], a); add(cmx, mx[i], a, 1); } reverse(adj[c].begin(), adj[c].end()); cmx = -1; a = 0; for (int i : adj[c]) { if (i == p) continue; add(up[i], cmx + 2, num[i], a); add(cmx, mx[i], a, 1); } for (int i : adj[c]) { if (i == p) continue; dfs2(i, c); } } inline void solve() { cin >> n; for (int x = 0; x < n - 1; x++) { int a, b; cin >> a >> b; adj[a].push_back(b); adj[b].push_back(a); } m = 0; for (int x = 1; x <= n; x++) { if (adj[x].size() == 1) m++; } cnt = ans = 0; cnt = m * (m - 1) / 2; dfs1(1, 0); dfs2(1, 0); cout << ans << " " << cnt << "\n"; } signed main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t = 1; // cin >> t; for (int x = 1; x <= t; x++) { solve(); } return 0; }