//clever
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
struct custom_hash
{
template<class T>
unsigned long long operator()(T v) const
{
unsigned long long x = v;
x += FIXED_RANDOM;
// x += 11400714819323198485ull;
// x = (x ^ (x >> 30)) * 13787848793156543929ull;
x = (x ^ (x >> 27)) * 10723151780598845931ull;
return x ^ (x >> 31);
}
};
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;
template<class T>
T randomize(T mod)
{
return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
x = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
x = x * 10 + (c - '0');
c = getchar();
}
if (negative)
{
x = -x;
}
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int buf[20], n = 0;
while(output)
{
buf[n] = ((output % 10));
output /= 10;
n++;
}
for (n--; n >= 0; n--)
{
putchar(buf[n] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
return (b ? gcd(b, a % b) : a);
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 500013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;
int N;
vi edge[MAXN];
pll ans = {0, 0};
int depth[MAXN];
pll dp[MAXN];
int dist[2][MAXN];
int parent[MAXN];
int S, T;
bool flag;
bitset<MAXN> diam;
void comb(pll &p, pll q)
{
if (q.se == 0) return;
if (q.fi > p.fi) p = q;
else if (q.fi == p.fi) p.se += q.se;
}
void gendist(int u)
{
FOR(i, 0, N) depth[i] = INF;
depth[u] = 0;
vi nodes;
nodes.PB(u);
while(!nodes.empty())
{
int v = nodes.back();
nodes.pop_back();
for (int w : edge[v])
{
if (depth[w] != INF) continue;
depth[w] = depth[v] + 1;
nodes.PB(w);
}
}
return;
}
void dfs(int u, int p)
{
parent[u] = p;
if (SZ(edge[u]) == 1)
{
dp[u] = MP(dist[flag][u], 1);
return;
}
dp[u] = MP(0, 0);
for (int v : edge[u])
{
if (v == p) continue;
dfs(v, u);
comb(dp[u], dp[v]);
}
ll tot = 0; int freq = 0;
for (int v : edge[u])
{
if (v == p) continue;
if (dp[v].fi == dp[u].fi)
{
freq++;
tot += dp[v].se;
}
}
pll opt = {0, 0};
if (freq > 1)
{
opt.fi = 1ll * dist[flag][u] * (dp[u].fi + dp[u].fi - 2 * dist[flag][u]);
for (int v : edge[u])
{
if (v == p) continue;
if (dp[v].fi == dp[u].fi)
{
opt.se += (tot - dp[v].se) * (dp[v].se);
}
}
opt.se /= 2;
}
else if (freq == 1)
{
for (int v : edge[u])
{
if (v == p) continue;
if (dp[v].fi != dp[u].fi)
{
comb(opt, dp[v]);
}
}
opt.se *= tot;
opt.fi = 1ll * dist[flag][u] * (opt.fi + dp[u].fi - 2 * dist[flag][u]);
}
comb(ans, opt);
}
void dfs3(int u)
{
if (SZ(edge[u]) == 1)
{
dp[u] = MP(dist[flag][u], 1);
return;
}
dp[u] = MP(0, 0);
for (int v : edge[u])
{
if (diam[v] || v == parent[u]) continue;
parent[v] = u;
dfs3(v);
comb(dp[u], dp[v]);
}
if (dist[0][u] == dist[1][u])
{
ll tot = 0; int freq = 0;
for (int v : edge[u])
{
if (diam[v] || v == parent[u]) continue;
if (dp[v].fi == dp[u].fi)
{
freq++;
tot += dp[v].se;
}
}
pll opt = {0, 0};
if (freq > 1)
{
opt.fi = 1ll * dist[flag][u] * (dp[u].fi + dp[u].fi - 2 * dist[flag][u]);
for (int v : edge[u])
{
if (diam[v] || v == parent[u]) continue;
if (dp[v].fi == dp[u].fi)
{
opt.se += (tot - dp[v].se) * (dp[v].se);
}
}
opt.se /= 2;
}
else if (freq == 1)
{
//find the second biggest!
for (int v : edge[u])
{
if (diam[v] || v == parent[u]) continue;
if (dp[v].fi != dp[u].fi)
{
comb(opt, dp[v]);
}
}
opt.se *= tot;
opt.fi = 1ll * dist[flag][u] * (opt.fi + dp[u].fi - 2 * dist[flag][u]);
}
if (opt.fi == ans.fi) ans.se -= opt.se;
}
}
void mark(int u, int p)
{
for (int v : edge[u])
{
if (diam[v] || v == p) continue;
depth[v] = depth[u] + 1;
mark(v, u);
}
}
int32_t main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
// if (fopen("file.in", "r"))
// {
// freopen ("file.in", "r", stdin);
// freopen ("file.out", "w", stdout);
// }
cin >> N;
FOR(i, 0, N - 1)
{
int u, v;
cin >> u >> v;
u--; v--;
edge[u].PB(v); edge[v].PB(u);
}
gendist(0);
FOR(i, 0, N)
{
if (depth[i] > depth[S])
{
S = i;
}
}
vi nodes;
nodes.PB(S);
while(!nodes.empty())
{
int v = nodes.back();
nodes.pop_back();
for (int w : edge[v])
{
if (w == S || dist[0][w]) continue;
dist[0][w] = dist[0][v] + 1;
nodes.PB(w);
}
}
FOR(i, 0, N)
{
if (dist[0][i] > dist[0][T]) T = i;
}
nodes.PB(T);
while(!nodes.empty())
{
int v = nodes.back();
nodes.pop_back();
for (int w : edge[v])
{
if (w == T || dist[1][w]) continue;
dist[1][w] = dist[1][v] + 1;
nodes.PB(w);
}
}
flag = true;
for (int v : edge[T])
{
dfs(v, T);
}
parent[S] = N;
flag = false;
for (int v : edge[S])
{
dfs(v, S);
}
vi lol;
int tmp = T;
while(tmp != S)
{
diam[tmp] = true;
lol.PB(tmp);
tmp = parent[tmp];
}
diam[tmp] = true;
lol.PB(tmp);
FOR(i, 0, N) depth[i] = 0;
FOR(i, 0, N)
{
if (!diam[i]) continue;
for (int v : edge[i])
{
if (diam[v]) continue;
depth[v] = 1;
mark(v, i);
}
}
tmp = 0;
FOR(i, 0, N) ckmax(tmp, depth[i]);
comb(ans, {1ll * dist[0][T] * tmp, 1});
if (SZ(lol) % 2)
{
int mid = lol[SZ(lol) / 2];
diam[mid] = false;
FOR(i, 0, N) parent[i] = N;
dfs3(mid);
}
cout << ans.fi << ' ' << ans.se << '\n';
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/
