// author: Nardos Wehabe
#include "bits/stdc++.h"
#ifndef ONLINE_JUDGE
#include "./debug/debug.h"
#endif
using namespace std;
typedef long long ll;
typedef map<int, int, greater<>> mapg;
// typedef __int128 lll;
void chmx(int n, int& mx1, int& mx2) {
if (n > mx1) {
mx2 = mx1;
mx1 = n;
} else mx2 = max(n, mx2);
}
void chmx2(int n, int& mx1, int& mx2, int& mx3) {
if (n > mx1) {
mx3 = mx2;
mx2 = mx1;
mx1 = n;
} else chmx(n, mx2, mx3);
}
void convert3(mapg& cnts, array<array<int, 2>, 3>& cur) {
int i = 0;
for (auto& [n, fq] : cnts) {
cur[i++] = { n, fq };
if (i >= 3) return;
}
}
void convert6(mapg& cnts, mapg& cur) {
int i = 0;
for (auto& [n, fq] : cnts) {
cur[n] = fq;
if (++i >= 6) return;
}
}
void incr(array<array<int, 2>, 3>& cur) {
cur[0][0]++;
cur[0][1] += cur[0][0] == 1;
cur[1][0] += cur[1][0] != 0;
cur[2][0] += cur[2][0] != 0;
}
void solve() {
int N;
cin >> N;
vector<int> adj[N];
for (int i = 0; i < N - 1; ++i) {
int u, v;
cin >> u >> v;
u--, v--;
adj[v].push_back(u);
adj[u].push_back(v);
}
vector<array<array<int, 2>, 3>> mxs(N, { {0, 0} });
function<array<array<int, 2>, 3>(int, int)> dfs1 = [&](int v, int p) {
mapg cnts;
for (auto ch : adj[v]) {
if (ch == p) continue;
auto ret = dfs1(ch, v);
for (auto [n, fq] : ret) cnts[n] += fq;
}
convert3(cnts, mxs[v]);
incr(mxs[v]);
return mxs[v];
};
dfs1(0, -1);
vector<array<ll, 2>> ans(N, { 0 });
ll best = 0;
function<void(int, int, array<array<int, 2>, 3>&)> dfs2 = [&](int v, int p, array<array<int, 2>, 3>& fr_p) {
mapg cur;
{
mapg cnts;
if (p != -1) mxs[p] = fr_p;
int mx1 = 0, mx2 = 0, mx3 = 0;
for (auto ch : adj[v]) {
auto ret = mxs[ch];
chmx2(ret[0][0], mx1, mx2, mx3);
for (auto [n, fq] : ret) cnts[n] += fq;
}
convert6(cnts, cur);
int cnt1 = cnts[mx1], cnt2 = cnts[mx2], cnt3 = cnts[mx3];
ans[v][0] = (1ll * (mx2 + mx3) * mx1) * (mx3 > 0);
best = max(ans[v][0], best);
if (mx2 == mx3) {
ans[v][1] = 1ll * cnt2 * (cnt2 - 1) / 2;
for (auto ch : adj[v]) {
auto ret = mxs[ch];
int fq = 0;
for (auto [n, f] : ret) {
fq += f * (n == mx2);
}
if (ret[0][0] == mx1 && ret[0][1] == cnt1) {
ans[v][1] -= 1ll * fq * (cnt2 - fq);
}
ans[v][1] -= 1ll * fq * (fq - 1) / 2;
}
} else {
ans[v][1] = 1ll * cnt2 * cnt3;
for (auto ch : adj[v]) {
auto ret = mxs[ch];
int fq1 = 0, fq2 = 0;
for (auto [n, fq] : ret) {
fq1 += fq * (n == mx2);
fq2 += fq * (n == mx3);
}
if (ret[0][0] == mx1 && ret[0][1] == cnt1) {
ans[v][1] -= 1ll * fq1 * (cnt3 - fq2) + 1ll * fq2 * (cnt2 - fq1);
}
ans[v][1] -= 1ll * fq1 * fq2;
}
}
}
for (auto ch : adj[v]) {
if (ch == p) continue;
auto ret = mxs[ch];
auto cur2 = cur;
for (auto [n, fq] : ret) {
cur2[n] -= fq;
if (cur2[n] == 0) cur2.erase(n);
}
array<array<int, 2>, 3> to_ch = { {0, 0} };
convert3(cur2, to_ch);
incr(to_ch);
dfs2(ch, v, to_ch);
}
};
array<array<int, 2>, 3> ne = { {0, 0} };
dfs2(0, -1, ne);
if (best == 0) {
cout << "0 1\n";
return;
}
ll cnt = 0;
for (auto [v, fq] : ans) {
if (v == best) cnt += fq;
assert(fq >= 0);
}
cout << best << " " << cnt << "\n";
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int tt = 1;
// cin >> tt;
while (tt--)
solve();
}
