#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int MAXN = 5e5 + 10;
pair<ll, ll> dp_1[MAXN], dp_2[MAXN];
vector<int> adj[MAXN];
pair<ll, ll> ans;
void dfs_1(int v, int p){
dp_1[v] = {-1e9, 0};
if(adj[v].size() == 1) dp_1[v] = {0, 1};
for(auto u : adj[v]){
if(u != p){
dfs_1(u, v);
if(dp_1[u].first + 1 > dp_1[v].first){
dp_1[v] = {dp_1[u].first + 1, dp_1[u].second};
} else if(dp_1[u].first + 1 == dp_1[v].first) dp_1[v].second += dp_1[u].second;
}
}
// cout << v << " -> " << dp_1[v].first << " " << dp_1[v].second << endl;
}
void dfs_2(int v, int p){
// cout << v << " -> " << dp_2[v].first << " " << dp_2[v].second << endl;
map<ll, ll> freq;
for(auto u : adj[v]){
if(u != p){
freq[dp_1[u].first + 1] += dp_1[u].second;
}
}
for(auto u : adj[v]){
if(u != p){
dp_2[u] = {dp_2[v].first + 1, dp_2[v].second};
freq[dp_1[u].first + 1] -= dp_1[u].second;
if(freq[dp_1[u].first + 1] == 0) freq.erase(dp_1[u].first + 1);
if(!freq.empty()){
auto [d, cnt] = *freq.rbegin();
if(d + 1 > dp_2[u].first){
dp_2[u] = {d + 1, cnt};
} else if(d + 1 == dp_2[u].first) dp_2[u].second += cnt;
}
freq[dp_1[u].first + 1] += dp_1[u].second;
}
}
freq.clear();
for(auto u : adj[v]) if(u != p) dfs_2(u, v);
}
void dfs_3(int v, int p){
for(auto u : adj[v]) if(u != p) dfs_3(u, v);
vector<pair<ll, ll>> choices;
for(auto u : adj[v]){
if(u != p){
choices.push_back({dp_1[u].first + 1, dp_1[u].second});
}
}
choices.push_back(dp_2[v]);
if(choices.size() < 3) return;
sort(choices.rbegin(), choices.rend());
pair<ll, ll> cur = {0, 0};
ll a = choices[0].first, b = choices[1].first, c = choices[2].first;
cur.first = a * (b + c);
if(a == b && b == c){
ll tot = 0;
for(auto [x, cnt] : choices) if(x == a) tot += cnt;
for(auto [x, cnt] : choices){
if(x == a){
cur.second += cnt * (tot - cnt);
}
}
cur.second /= 2;
} else if(a == b){
ll tot_b = 0, tot_c = 0;
for(auto [x, cnt] : choices){
if(x == b) tot_b += cnt;
if(x == c) tot_c += cnt;
}
cur.second += tot_b * tot_c;
} else if(b == c){
ll tot = 0;
for(auto [x, cnt] : choices) if(x == b) tot += cnt;
for(auto [x, cnt] : choices){
if(x == b){
cur.second += cnt * (tot - cnt);
}
}
cur.second /= 2;
} else{
ll tot_b = 0, tot_c = 0;
for(auto [x, cnt] : choices){
if(x == b) tot_b += cnt;
if(x == c) tot_c += cnt;
}
cur.second += tot_b * tot_c;
}
if(cur.first > ans.first){
ans = cur;
} else if(cur.first == ans.first) ans.second += cur.second;
}
int main(){
cin.tie(0)->sync_with_stdio(0);
int n; cin >> n;
for(int i=1; i<=n; i++) dp_2[i] = {-1e9, 0};
for(int i=1; i<n; i++){
int a, b; cin >> a >> b;
adj[a].push_back(b);
adj[b].push_back(a);
}
dfs_1(1, 1);
if(adj[1].size() == 1) dp_2[1] = {0, 1};
dfs_2(1, 1);
ans = {0, 0};
dfs_3(1, 1);
ll leaves = 0;
for(int i=1; i<=n; i++) leaves += (adj[i].size() == 1);
if(ans.first == 0) ans.second = (leaves * (leaves - 1)) / 2;
cout << ans.first << " " << ans.second << "\n";
return 0;
}
