// dmoj problem: https://vjudge.net/contest/757167#problem/K
#include <bits/stdc++.h>
#define int long long
#define MOD 1000000007
using namespace std;
int n, out, amnt;
pair<int, int> dist[500001];
vector<int> adjList[500001];
void dfs(int node, int last)
{
dist[node] = {0, 1};
for (int u : adjList[node])
{
if (u != last)
{
dfs(u, node);
if (dist[u].first + 1 > dist[node].first)
dist[node] = {dist[u].first + 1, dist[u].second};
else if (dist[u].first + 1 == dist[node].first)
dist[node].second += dist[u].second;
}
}
}
void reroot(int node, int last, int before, int waysbefore)
{
vector<pair<int, int>> options;
if (before != 0)
options.push_back({before, waysbefore});
for (int u : adjList[node])
if (u != last)
options.push_back({dist[u].first + 1, dist[u].second});
sort(options.begin(), options.end());
if (options.size() == 1)
{
if (out == 0)
amnt += waysbefore;
// this will overcount x2
}
if (options.size() == 2)
{
} // overcount
if (options.size() >= 3)
{
int candout = options[options.size() - 1].first * (options[options.size() - 2].first + options[options.size() - 3].first);
if (candout > out)
{
out = candout;
amnt = 0;
}
if (candout == out)
{
pair<int, int> want = {-1, -1};
want.first = options[options.size() - 2].first;
if (options[options.size() - 3].first != want.first)
want.second = options[options.size() - 3].first;
pair<int, int> sums;
int delta = 0;
for (int i = 0; i < options.size(); i++)
{
if (options[i].first == want.first)
sums.first += options[i].second;
if (options[i].first == want.second)
sums.second += options[i].second;
}
if (want.second != -1)
delta += sums.first * sums.second;
else
{
delta += sums.first * sums.first;
for (int i = 0; i < options.size(); i++)
if (options[i].first == want.first)
delta -= options[i].second * options[i].second;
delta /= 2;
}
amnt += delta;
}
}
int amntbest = 0;
int sb = -1;
int amntsecondbest = 0;
for (int i = options.size() - 1; i >= 0; i--)
{
if (options[i].first == options.back().first)
amntbest += options[i].second;
else if (sb == -1)
sb = options[i].first;
if (options[i].first == sb)
amntsecondbest += options[i].second;
}
for (int u : adjList[node])
if (u != last)
{
if (dist[u].first + 1 == options.back().first)
{
if (amntbest - dist[u].second > 0)
reroot(u, node, options.back().first + 1, amntbest - dist[u].second);
else
reroot(u, node, sb + 1, amntsecondbest);
}
else
reroot(u, node, options.back().first + 1, amntbest);
}
}
int32_t main()
{
cin.sync_with_stdio(0);
cin.tie(0);
cin >> n;
for (int i = 0; i < n - 1; i++)
{
int a, b;
cin >> a >> b;
adjList[a].push_back(b);
adjList[b].push_back(a);
}
if (n == 2)
{
cout << "0 1" << "\n";
return 0;
}
for (int i = 1; i <= n; i++)
{
if (adjList[i].size() != 1)
{
dfs(i, 0);
reroot(i, 0, 0, 1);
break;
}
}
cout << out << " ";
cout << (out == 0 ? amnt / 2 : amnt) << "\n";
return 0;
}
