//
// Created by liasa on 15/11/2025.
//
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define v vector
#define lp(i, s, e) for (ll i = s; i < e; ++i)
ll n;
v<v<ll>> g;
#define pll pair<ll, ll>
v<pll> dp, dpp;
const ll inf = 1e18;
pll merge(pll a, pll b) {
if (b.first > a.first)
return b;
if (b.first < a.first)
return a;
return {a.first, a.second + b.second};
}
void dfs(ll node, ll par) {
if (g[node].size() == 1 && par != -1) {
dp[node] = {0, 1};
}
for (auto it : g[node]) {
if (it != par) {
dfs(it, node);
pll cand = {dp[it].first + 1, dp[it].second};
dp[node] = merge(dp[node], cand);
}
}
}
void dfs2(ll node, ll par) {
v<ll> kids;
for (auto it : g[node])
if (it != par)
kids.push_back(it);
v<pll> suf(kids.size() + 1, {-inf, 0});
for (ll i = (ll)kids.size() - 1; i >= 0; --i) {
pll add = {dp[kids[i]].first + 2, dp[kids[i]].second};
suf[i] = merge(add, suf[i + 1]);
}
pll left = {dpp[node].first + 1, dpp[node].second};
lp(i, 0, (ll)kids.size()) {
pll cur = merge(left, suf[i + 1]);
dpp[kids[i]] = merge(dpp[kids[i]], cur);
pll add = {dp[kids[i]].first + 2, dp[kids[i]].second};
left = merge(left, add);
}
for (auto it : g[node])
if (it != par)
dfs2(it, node);
}
ll ans = 0, cnt = 0;
void dfs3(ll node, ll par) {
v<pll> a;
for (auto it : g[node])
if (it != par) {
pll q = {dp[it].first + 1, dp[it].second};
if (q.second > 0)
a.push_back(q);
}
if (par != -1 && dpp[node].second > 0)
a.push_back(dpp[node]);
if (a.size() >= 3) {
sort(a.begin(), a.end(), [](const pll &x, const pll &y) {
if (x.first != y.first)
return x.first > y.first;
return x.second > y.second;
});
ll val = 0;
ll ways = 0;
if (a[1].first != a[2].first) {
ll n1 = 0, n2 = 0;
for (auto &p : a) {
if (p.first == a[1].first)
n1 += p.second;
else if (p.first == a[2].first)
n2 += p.second;
else if (p.first < a[2].first)
break;
}
val = a[0].first * (a[1].first + a[2].first);
ways = n1 * n2;
} else {
ll n1 = 0, n2 = 0;
for (auto &p : a) {
if (p.first == a[1].first) {
n2 += n1 * p.second;
n1 += p.second;
} else if (p.first < a[1].first)
break;
}
val = a[0].first * a[1].first * 2;
ways = n2;
}
if (ways > 0) {
if (val > ans) {
ans = val;
cnt = ways;
} else if (val == ans) {
cnt += ways;
}
}
}
for (auto it : g[node])
if (it != par)
dfs3(it, node);
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n;
g.resize(n);
lp(i, 0, n - 1) {
ll a, b;
cin >> a >> b;
a--;
b--;
g[a].push_back(b);
g[b].push_back(a);
}
ll O = 0, T = 0;
lp(i, 0, n) {
if (g[i].size() == 1)
O++;
if (g[i].size() == 2)
T++;
}
if (O == 2 && T == n - 2 || n == 2) {
cout << 0 << " " << 1 << "\n";
return 0;
}
dp.resize(n, {-inf, 0});
dpp.resize(n, {-inf, 0});
dpp[0] = {(g[0].size() == 1) ? 0 : -inf, (g[0].size() == 1) ? 1 : 0};
dfs(0, -1);
dfs2(0, -1);
dfs3(0, -1);
cout << ans << " " << cnt << "\n";
}
