#include<bits/stdc++.h>
#define int long long
#define ii pair<int,int>
#define ff first
#define ss second
using namespace std;
const int maxn = 5e5 + 5;
int n;
ii res, dp[maxn];
vector<int> adj[maxn];
inline ii upd(ii a, int x, int y)
{
if (a.ff < x)
a = {x, y};
else if (a.ff == x)
a.ss += y;
return a;
}
void dfs(int x = 1, int p = 1)
{
dp[x].ss = 1;
for (int i : adj[x]) if (i != p)
{
dfs(i, x);
dp[x] = upd(dp[x], dp[i].ff + 1, dp[i].ss);
}
}
void reroot(int x = 1, int p = 1, ii fp = {0, 1})
{
vector<ii> pre = {fp}, suf = {{0, 0}}, cand;
if (x > 1 || adj[x].size() == 1)
cand.emplace_back(fp);
for (int i : adj[x]) if (i != p)
cand.emplace_back(dp[i].ff + 1, dp[i].ss);
sort(cand.begin(), cand.end(), greater<ii>());
if (cand.size() >= 3)
{
int hardness = cand[0].ff * (cand[1].ff + cand[2].ff), ways = 0, tmp = 0;
for (auto i : cand) if (i.ff == cand[2].ff) tmp += i.ss;
if (cand[1].ff == cand[2].ff)
{
ways = tmp * tmp;
for (auto i : cand) if (i.ff == cand[2].ff)
ways -= i.ss * i.ss;
ways /= 2;
}
else if (cand[0].ff == cand[1].ff)
{
ways = (cand[0].ss + cand[1].ss) * tmp;
} else ways = cand[1].ss * tmp;
res = upd(res, hardness, ways);
}
for (int i : adj[x]) if (i != p) pre.emplace_back(upd(pre.back(), dp[i].ff + 1, dp[i].ss));
for (int j = (int)adj[x].size() - 1; j >= 0; j--)
{
int i = adj[x][j];
if (i == p) continue;
suf.emplace_back(upd(suf.back(), dp[i].ff + 1, dp[i].ss));
}
reverse(suf.begin(), suf.end());
int cnt = 0;
for (int i : adj[x]) if (i != p)
{
pre[cnt].ff++;
ii xx = upd(pre[cnt], suf[cnt + 1].ff + 1, suf[cnt + 1].ss);
reroot(i, x, xx);
cnt++;
}
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
// freopen("test.inp", "r", stdin);
// freopen("test.out", "w", stdout);
cin >> n;
for (int i = 1, u, v; i < n; i++)
cin >> u >> v,
adj[u].emplace_back(v),
adj[v].emplace_back(u);
dfs();
reroot();
cout << res.ff << " " << max(1ll, res.ss);
}
