//Huyduocdithitp
#include <bits/stdc++.h>
typedef long long ll;
#define pii pair<ll, ll>
#define MP make_pair
#define fi first
#define se second
#define TASK "mansion"
#define start if(fopen(TASK".in","r")){freopen(TASK".in","r",stdin);freopen(TASK".out","w",stdout);}
#define faster ios_base::sync_with_stdio(false);cin.tie(NULL);
#define N 200005
#define LOG 19
#define endl '\n'
using namespace std;
bool ghuy4g;
ll n;
vector<ll> adj[N];
ll d[N][2], c[N][2];
pii ans;
void dfs(ll u, ll parent) {
vector<pii> vt;
for (auto v : adj[u]) {
if (v == parent) continue;
dfs(v, u);
//vt.push_back({d[v][0] + 1, c[v][0]});
d[v][0] ++ ;
if (d[v][0] >= d[u][0]) {
d[u][1] = d[u][0];
d[u][0] = d[v][0];
}
else if (d[v][0] >= d[u][1]) {
d[u][1] = d[v][0];
}
d[v][0] -- ;
}
for (auto v : adj[u]) {
if (v == parent) continue;
if (d[v][0] + 1 == d[u][0]) {
c[u][0] += c[v][0];
}
if (d[v][0] + 1 == d[u][1]) {
c[u][1] += c[v][0];
}
}
if (d[u][0] == 0) {
c[u][0] = 1;
}
if (d[u][1] == 0) {
c[u][1] = 1;
}
}
void reroot(ll u, ll parent) {
vector<pii> vt;
for (auto v : adj[u]) {
vt.push_back({d[v][0] + 1, c[v][0]});
}
pii cnt = {0, 0}; // cnt.fi la ket qua, cnt.se la so con dai bang con thu 2
if (adj[u].size() >= 3) {
sort(vt.begin(), vt.end(), greater<pii>());
ll x = vt[0].fi * (vt[1].fi + vt[2].fi);
for (pii it : vt) {
if (u == 2) {
//cout << it.fi << " " << it.se << endl;
}
// ta dang thu chon con it nay la con thu 2
// => no se gop voi cac con bang con thu nhat dang truoc
// 0 = 1 = 2 van duoc, vi luon luon co 1 con lam nhanh dai nhat
if (it.fi == vt[2].fi) {
cnt.fi += cnt.se * it.se;
}
if (it.fi == vt[1].fi) {
cnt.se += it.se;
}
}
if (x > ans.fi) {
ans.fi = x;
ans.se = cnt.fi;
}
else if (x == ans.fi) {
ans.se += cnt.fi;
}
}
for (auto v : adj[u]) {
if (v == parent) continue;
ll dv0 = d[v][0], cv0 = c[v][0], du0 = d[u][0], cu0 = c[u][0], dv1 = d[v][1], cv1 = c[v][1];
if (d[v][0] + 1 == d[u][0]) {
if (c[v][0] == c[u][0]) { // nhanh to nhat la nhanh nay luon, khong co thu 2
d[u][0] = d[u][1];
c[u][0] = c[u][1];
}
else {
c[u][0] -= c[v][0];
}
}
if (d[u][0] + 1 >= d[v][0]) {
d[v][1] = d[v][0]; c[v][1] = c[v][0];
d[v][0] = d[u][0] + 1;
c[v][0] = c[u][0];
}
reroot(v, u);
d[v][0] = dv0, c[v][0] = cv0, d[u][0] = du0, c[u][0] = cu0, d[v][1] = dv1, c[v][1] = cv1;
}
}
bool klinh;
signed main(void) {
faster;
cin >> n;
for (int i = 1; i <= n - 1; i ++) {
ll u, v;
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
ll r = 1;
dfs(r, r);
reroot(r, r);
if (ans.fi == 0) ans.se = 1;
cout << ans.fi << " " << ans.se;
cerr << fabs(&klinh - &ghuy4g) / double(1024 * 1024);
return 0;
}
