// 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 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<int> mxh(N), cnts(N);
function<void(int, int)> dfs1 = [&](int v, int p) {
for (auto ch : adj[v]) {
if (ch == p) continue;
dfs1(ch, v);
if (mxh[ch] > mxh[v]) {
mxh[v] = mxh[ch];
cnts[v] = cnts[ch];
} else if (mxh[ch] == mxh[v]) cnts[v] += cnts[ch];
}
mxh[v]++;
cnts[v] += mxh[v] == 1;
};
dfs1(0, -1);
vector<array<ll, 2>> ans(N, { 0 });
ll best = 0;
function<void(int, int, int, int)> dfs2 = [&](int v, int p, int pmx, int pcnt) {
int mx1 = pmx, mx2 = 0, mx3 = 0;
int cnt1 = 0, cnt2 = 0, cnt3 = 0;
{
vector<array<int, 2>> mxs{ {pmx, pcnt} };
for (auto ch : adj[v]) {
if (ch == p) continue;
mxs.push_back({ mxh[ch], cnts[ch] });
chmx2(mxh[ch], mx1, mx2, mx3);
}
for (auto [n, fq] : mxs) {
cnt1 += fq * (n == mx1);
cnt2 += fq * (n == mx2);
cnt3 += fq * (n == mx3);
}
ans[v][0] = (1ll * (mx2 + mx3) * mx1) * (mx3 > 0);
best = max(ans[v][0], best);
if (best && ans[v][0] == best) {
if (mx2 == mx3) {
ans[v][1] += 1ll * cnt2 * (cnt2 - 1) / 2;
for (auto [n, fq] : mxs) {
if (n == mx2) ans[v][1] -= 1ll * fq * (fq - 1) / 2;
}
} else {
ans[v][1] = 1ll * cnt2 * cnt3;
}
}
}
for (auto ch : adj[v]) {
if (ch == p) continue;
int chmx = mx1, chcnt = cnt1;
if (mxh[ch] == mx1 && cnts[ch] == cnt1) {
chmx = mx2, chcnt = cnt2;
} else if (mxh[ch] == mx1) {
chmx = mx1, chcnt = cnt1 - cnts[ch];
}
chmx++;
chcnt += chmx == 1;
dfs2(ch, v, chmx, chcnt);
}
};
dfs2(0, -1, 0, 0);
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();
}
