// author: Nardos Wehabe
#include "bits/stdc++.h"
#ifndef ONLINE_JUDGE
#include "./debug/debug.h"
#endif
using namespace std;
typedef long long ll;
// 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<array<int, 6>> mxs(N, { 0 });
function<array<int, 6>(int, int)> dfs1 = [&](int v, int p) {
vector<array<int, 2>> cnts;
for (auto ch : adj[v]) {
if (ch == p) continue;
auto [n1, c1, n2, c2, n3, c3] = dfs1(ch, v);
if (!n1) continue;
cnts.push_back({ n1, c1 });
if (!n2) continue;
cnts.push_back({ n2, c2 });
if (!n3) continue;
cnts.push_back({ n3, c3 });
}
sort(cnts.begin(), cnts.end(), [](const array<int, 2>& lhs, const array<int, 2>& rhs) {
return lhs[0] > rhs[0];
});
int j = 0, i = 0, L = cnts.size();
while (i < L && j < 3) {
int n = cnts[i][0], fq = cnts[i++][1];
while (i < L && cnts[i][0] == n) {
fq += cnts[i++][1];
}
mxs[v][2 * j] = n;
mxs[v][2 * j + 1] = fq;
j++;
}
auto& ret = mxs[v];
ret[0]++;
ret[1] += adj[v].size() == 1;
ret[2] += ret[2] != 0;
ret[4] += ret[4] != 0;
return ret;
};
dfs1(0, -1);
vector<array<ll, 2>> ans(N, { 0 });
ll best = 0;
function<void(int, int, array<int, 6>&)> dfs2 = [&](int v, int p, array<int, 6>& fr_p) {
array<int, 12> cur{ 0 };
{
vector<array<int, 2>> cnts;
auto [n1, c1, n2, c2, n3, c3] = fr_p;
if (n1) cnts.push_back({ n1, c1 });
if (n2) cnts.push_back({ n2, c2 });
if (n3) cnts.push_back({ n3, c3 });
int mx1 = n1, mx2 = 0, mx3 = 0;
for (auto ch : adj[v]) {
if (ch == p) continue;
auto [n1, c1, n2, c2, n3, c3] = mxs[ch];
chmx2(n1, mx1, mx2, mx3);
if (!n1) continue; cnts.push_back({ n1, c1 });
if (!n2) continue; cnts.push_back({ n2, c2 });
if (!n3) continue; cnts.push_back({ n3, c3 });
}
sort(cnts.begin(), cnts.end(), [](const array<int, 2>& lhs, const array<int, 2>& rhs) {
return lhs[0] > rhs[0];
});
int cnt1 = 0, cnt2 = 0, cnt3 = 0;
int i = 0, j = 0, L = cnts.size();
while (i < L) {
int n = cnts[i][0], fq = cnts[i++][1];
while (i < L && cnts[i][0] == n) {
fq += cnts[i++][1];
}
cnt1 += fq * (n == mx1);
cnt2 += fq * (n == mx2);
cnt3 += fq * (n == mx3);
if (j < 6) {
cur[j * 2] = n;
cur[j * 2 + 1] = fq;
j++;
}
}
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;
if (n1 == mx2) {
ans[v][1] -= 1ll * c1 * (c1 - 1) / 2;
} else if (n2 == mx2) {
ans[v][1] -= 1ll * c2 * (c2 - 1) / 2;
} else if (n3 == mx2) {
ans[v][1] -= 1ll * c3 * (c3 - 1) / 2;
}
for (auto ch : adj[v]) {
if (ch == p) continue;
auto [n1, c1, n2, c2, n3, c3] = mxs[ch];
int fq = c1 * (n1 == mx2) + c2 * (n2 == mx2) + c3 * (n3 == mx3);
if (n1 == mx1 && c1 == cnt1) {
ans[v][1] -= 1ll * fq * (cnt2 - fq);
}
ans[v][1] -= 1ll * fq * (fq - 1) / 2;
}
} else {
ans[v][1] = 1ll * cnt2 * cnt3;
int fq1 = c1 * (n1 == mx2) + c2 * (n2 == mx2) + c3 * (n3 == mx2);
int fq2 = c1 * (n1 == mx3) + c2 * (n2 == mx3) + c3 * (n3 == mx3);
ans[v][1] -= 1ll * fq1 * fq2;
for (auto ch : adj[v]) {
if (ch == p) continue;
auto [n1, c1, n2, c2, n3, c3] = mxs[ch];
int fq1 = c1 * (n1 == mx2) + c2 * (n2 == mx2) + c3 * (n3 == mx2);
int fq2 = c1 * (n1 == mx3) + c2 * (n2 == mx3) + c3 * (n3 == mx3);
if (n1 == mx1 && c1 == 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;
array<int, 6> to_ch{ 0 };
auto [n1, c1, n2, c2, n3, c3] = mxs[ch];
int j = 0;
for (int i = 0; i < 6; ++i) {
int n = cur[2 * i], fq = cur[2 * i + 1];
fq -= c1 * (n1 == n) + c2 * (n == n2) + c3 * (n == n3);
if (fq) {
to_ch[2 * j] = n;
to_ch[2 * j + 1] = fq;
j++;
}
if (j >= 3) break;
}
to_ch[0]++;
to_ch[1] += (to_ch[0] == 1);
to_ch[2] += to_ch[2] != 0;
to_ch[4] += to_ch[4] != 0;
dfs2(ch, v, to_ch);
}
};
array<int, 6> ne = { 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();
}
