#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<int> adj[500001];
int up[500001], down[500001];
ll upFreq[500001], downFreq[500001];
ll ans = 0;
ll freq = 1;
void update(ll x, ll f)
{
if (x > ans)
ans = x, freq = f;
else if (x == ans)
freq += f;
}
void dfs(int node, int p)
{
downFreq[node] = upFreq[node] = 1;
for (int i : adj[node])
{
if (i == p)
continue;
dfs(i, node);
if (down[node] < down[i] + 1)
down[node] = down[i] + 1, downFreq[node] = downFreq[i];
else if (down[node] == down[i] + 1)
downFreq[node] += downFreq[i];
}
}
void dfs1(int node, int p)
{
vector<array<ll, 2>> paths;
paths.push_back({up[node], upFreq[node]});
for (int i : adj[node])
if (i != p)
paths.push_back({down[i] + 1, downFreq[i]});
sort(paths.rbegin(), paths.rend());
if (adj[node].size() > 2)
{
ll a = paths[0][0];
ll b = paths[1][0];
ll c = paths[2][0];
ll x = a * (b + c);
// all distinct
if (a != b && b != c)
{
ll cnt = 0;
for (auto [len, f] : paths)
if (len == c)
cnt += f;
update(x, paths[1][1] * cnt);
}
else if (a == b && b == c) // all same
{
ll cnt = 0;
ll res = 0;
for (auto [len, f] : paths)
if (len == c)
cnt += f;
// if (node == 2)
// cout << "HI " << cnt << endl;
for (auto [len, f] : paths)
if (len == c)
res += f * (cnt - f);
update(x, res / 2);
}
else if (a == b) // only first two are the same
{
ll cnt = 0;
for (auto [len, f] : paths)
if (len == c)
cnt += f;
update(x, (paths[0][1] + paths[1][1]) * cnt);
}
else if (b == c) // last two are the same
{
ll cnt = 0;
ll res = 0;
for (auto [len, f] : paths)
if (len == c)
cnt += f;
for (auto [len, f] : paths)
if (len == c)
res += f * (cnt - f);
update(x, res / 2);
}
}
ll best1 = 0, best2 = 0;
for (auto [len, f] : paths)
if (len == paths[0][0])
best1 += f;
for (auto [len, f] : paths)
if (len == paths[1][0])
best2 += f;
for (int i : adj[node])
{
if (i == p)
continue;
ll path = down[i] + 1;
if (path == paths[0][0])
{
best1 -= downFreq[i];
if (best1 == 0) // only 1 longest path
up[i] = paths[1][0] + 1, upFreq[i] = best2;
else
up[i] = paths[0][0] + 1, upFreq[i] = best1;
}
else
up[i] = paths[0][0] + 1, upFreq[i] = best1;
dfs1(i, node);
}
}
int main()
{
cin.tie(NULL) -> sync_with_stdio(false);
int N;
cin >> N;
while (--N)
{
int a, b;
cin >> a >> b;
adj[a].push_back(b);
adj[b].push_back(a);
}
dfs(1, 0);
dfs1(1, 0);
cout << ans << ' ' << freq << endl;
return 0;
}
