#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// #include <ext/rope>
using namespace std;
// using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int uint;
typedef long double ld;
template <class T>
using VV = vector<vector<T>>;
using VI = vector<int>;
using VVI = vector<vector<int>>;
using VL = vector<long long>;
using VVL = vector<vector<long long>>;
using VC = vector<char>;
using VVC = vector<vector<char>>;
using VB = vector<bool>;
using VVB = vector<vector<bool>>;
using VD = vector<double>;
using VVD = vector<vector<double>>;
using PII = pair<int, int>;
using PLL = pair<long long, long long>;
using PIL = pair<int, long long>;
using PLI = pair<long long, int>;
using VPII = vector<pair<int, int>>;
using VPLL = vector<pair<long long, long long>>;
#define LINE '\n'
#define SPACE ' '
#define PB push_back
#define FOR(i, a, b) for (int i = (a); i < (int(b)); i++)
#define FORE(i, a, b) for (int i = (a); i <= (int)((b)); i++)
#define ALL(x) x.begin(), x.end()
#define RALL(x) x.rbegin(), x.rend()
#define sq(a) ((a) * (a))
#define sz(x) ((int)x.size())
#define fastio() \
ios_base::sync_with_stdio(false); \
cin.tie(nullptr); \
cout.tie(nullptr)
#define debug(x) cerr << #x << " = " << x << endl;
const ll MOD = 1e9 + 7;
template <class T>
inline void maxi(T &a, T b)
{
a = max(a, b);
}
template <class T>
inline void mini(T &a, T b)
{
a = min(a, b);
}
template <class T>
inline void addi(T &a, T b)
{
a = (a + b) % MOD;
}
template <class T>
inline void subi(T &a, T b)
{
a = (a - b + MOD) % MOD;
}
template <class T>
inline T add(T a, T b)
{
return (a + b) % MOD;
}
template <class T>
inline T sub(T a, T b)
{
return (a - b + MOD) % MOD;
}
template <class T>
inline T mul(T a, T b)
{
return ((a % MOD) * (b % MOD)) % MOD;
}
constexpr ll binpow(ll a, ll b, ll mod)
{
ll res = 1;
while (b > 0)
{
if (b & 1)
{
res = (res * a) % mod;
}
a = (a * a) % mod;
b >>= 1;
}
return res;
}
const int INF = 1e9;
const int MAX_N = 5e5 + 3;
int n;
VL dp(MAX_N, 0); // max dist down
VL ct(MAX_N, 1); // no of ways
VI g[MAX_N];
void dfs1(int c, int p)
{
ct[c]=1;
for (auto v : g[c])
{
if (v == p)
continue;
dfs1(v, c);
if (dp[v] + 1 > dp[c])
{
dp[c] = dp[v] + 1;
ct[c] = ct[v];
}
else if (dp[v] + 1 == dp[c])
{
ct[c] += ct[v];
}
}
}
ll ans_dist = 0;
ll ans_ct = 0;
void dfs2(int c, int p, ll up_dist, ll up_ways)
{
vector<PLL> vec;
if(c != 1 || sz(g[c]) == 1)
vec.PB({up_dist, up_ways});
for (auto v : g[c]) {
if(v != p) vec.PB({dp[v] + 1, ct[v]});
}
sort(RALL(vec));
if (sz(g[c]) >= 3)
{
ll dist = vec[0].first * (vec[1].first + vec[2].first);
ll ways = 0;
ll eq = 0; // sum of ways to get vec[2].dist
for (auto [d, w] : vec)
{
if (d == vec[2].first)
eq += w;
}
if (vec[1].first == vec[2].first)
{
// since vec[0] is the max dist, 1 and 2 are terminals
ways = eq * eq;
for (auto [d, w] : vec)
{
// delete duplicates(paths overlap)
if (d == vec[2].first)
ways -= sq(w);
}
// we need unique paths, (a, b) is the same as (b, a)
ways /= 2;
}
else if (vec[0].first == vec[1].first)
{
ways = eq * (vec[0].second + vec[1].second);
}
else
{
ways = vec[1].second * eq;
}
if (dist > ans_dist) {
ans_dist = dist;
ans_ct = ways;
}
else if (dist == ans_dist)
ans_ct += ways;
}
ll d1 = vec[0].first;
ll w1 = 0;
ll d2 = 0, w2 = 0;
if (sz(vec) >= 2)
{
d2 = vec[1].first;
}
w1 = w2 = 0;
for (auto [d, w] : vec)
{
if (d1 == d)
w1 += w;
if (d2 == d)
w2 += w;
}
maxi(w1, 1LL);
maxi(w2, 1LL);
for (auto v : g[c])
{
if (v == p)
continue;
if (dp[v] + 1 == d1)
{ // max paths goes trough
if (ct[v] == w1)
{
dfs2(v, c, d2 + 1, w2);
}
else {
dfs2(v, c, d1 + 1, w1 - ct[v]);
}
}
else
{
dfs2(v, c, d1 + 1, w1);
}
}
}
void solve()
{
cin >> n;
FOR(i, 0, n - 1)
{
int a, b;
cin >> a >> b;
g[a].PB(b);
g[b].PB(a);
}
dfs1(1, 1);
dfs2(1, 1, 0, 1);
if (ans_dist == 0)
ans_ct = 1;
cout << ans_dist << SPACE << ans_ct << LINE;
}
int main()
{
fastio();
int t = 1;
// cin >> t;
while (t--)
solve();
}
