#include<bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define in insert
#define all(x) x.begin(),x.end()
#define pb push_back
#define eb emplace_back
#define ff first
#define ss second
#define int long long
typedef long long ll;
typedef vector<int> vi;
typedef set<int> si;
typedef multiset<int> msi;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
template<typename T, typename U>
ostream & operator << (ostream &out, const pair<T, U> &c) {
out << c.first << ' ' << c.second;
return out;
}
template<typename T>
ostream & operator << (ostream &out, vector<T> &v) {
const int sz = v.size();
for (int i = 0; i < sz; i++) {
if (i) out << ' ';
out << v[i];
}
return out;
}
template<typename T>
istream & operator >> (istream &in, vector<T> &v) {
for (T &x : v) in >> x;
return in;
}
template<typename T>
void mxx(T &a, T b){if(b > a) a = b;}
template<typename T>
void mnn(T &a, T b){if(b < a) a = b;}
const int mxn = 5e5 + 10;
int n, ans1, ans2;
vector<int> g[mxn];
pair<int, int> d[mxn];
void init(int to, int fr) {
auto it = find(all(g[to]), fr);
if(it != g[to].end()) {
g[to].erase(it);
}
d[to] = {0, 1};
for(int x : g[to]) {
init(x, to);
if(d[x].ff + 1 > d[to].ff) {
d[to] = d[x];
d[to].ff++;
} else if(d[x].ff + 1 == d[to].ff) {
d[to].ss += d[x].ss;
}
}
}
void dfs(int to, int mx, int cnt) {
vector<pair<int, int>> v;
if(to != 1 && cnt) {
v.pb({mx, cnt});
}
for(int x : g[to]) {
v.pb({d[x].ff + 1, d[x].ss});
}
sort(v.rbegin(), v.rend());
if(v.size() >= 3) {
int nmx = (v[0].ff * (v[1].ff + v[2].ff)), ncnt = 0;
int sum = 0;
for(auto it : v) {
if(it.ff == v[2].ff) {
sum += it.ss;
}
}
if(v[1].ff == v[2].ff) {
ncnt = sum * sum;
for(auto it : v) {
if(it.ff == v[2].ff) {
ncnt -= it.ss * it.ss;
}
}
ncnt /= 2;
} else if(v[1].ff == v[0].ff) {
ncnt = (v[0].ss + v[1].ss) * sum;
} else {
ncnt = v[1].ss * sum;
}
if(nmx > ans1) {
ans1 = nmx;
ans2 = ncnt;
} else if(nmx == ans1) {
ans2 += ncnt;
}
}
pair<int, int> mx1, mx2;
mx1 = mx2 = make_pair(0, 0);
if(cnt) mx1 = make_pair(mx + 1, cnt);
for(int x : g[to]) {
if(d[x].ff + 2 > mx1.ff) {
mx2 = mx1;
mx1 = d[x];
mx1.ff += 2;
} else if(d[x].ff + 2 == mx1.ff) {
mx1.ss += d[x].ss;
} else if(d[x].ff + 2 > mx2.ff) {
mx2 = d[x];
mx2.ff += 2;
} else if(d[x].ff + 2 == mx2.ff) {
mx2.ss += d[x].ss;
}
}
for(int x : g[to]) {
if(d[x].ff + 2 == mx1.ff) {
if(d[x].ss == mx1.ss) {
dfs(x, mx2.ff, mx2.ss);
} else {
dfs(x, mx1.ff, mx1.ss - d[x].ss);
}
} else {
dfs(x, mx1.ff, mx1.ss);
}
}
}
void go() {
cin >> n;
for(int i = 1; i < n; i++) {
int x, y;
cin >> x >> y;
g[x].pb(y);
g[y].pb(x);
}
ans1 = 0;
ans2 = 1;
if(n == 2) {
cout << ans1 << ' ' << ans2 << '\n';
return;
}
int root = 1;
for(int i = 1; i <= n; i++) {
if(g[i].size() > 1) {
root = i;
}
}
init(root, 0);
dfs(root, 0, 0);
cout << ans1 << ' ' << ans2 << '\n';
}
signed main() {
// #ifndef ONO
// freopen("file.in", "r", stdin);
// freopen("file.out", "w", stdout);
// #endif
fast;
int t = 1;
// cin >> t;
while(t--) {
go();
}
return 0;
}
