#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ldb;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ldb,ldb> pdd;
#define ff(i,a,b) for(int i = a; i <= b; i++)
#define fb(i,b,a) for(int i = b; i >= a; i--)
#define trav(a,x) for(auto& a : x)
#define sz(a) (int)(a).size()
#define fi first
#define se second
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k) print the k-th smallest number in os(0-based)
const int mod = 1000000007;
const int inf = 1e9 + 5;
const int mxN = 500005;
int n;
vector<int> g[mxN];
int d[mxN];
int par[mxN];
void dfs1(int v, int p){
par[v] = p;
for(auto u : g[v]){
if(u != p){
d[u] = d[v] + 1; dfs1(u, v);
}
}
}
pll cmb(pll s1, pll s2){
if(s1.fi == s2.fi)return {s1.fi, s1.se + s2.se};
else return (s1.fi > s2.fi ? s1 : s2);
}
pll rez = {0, 0};
pii mx[mxN];
bool visited[mxN];
void dfs2(int v, int p, int dist){
if(sz(g[v]) == 1){
mx[v] = {d[v], 1};
return;
}
pii najv1 = {-inf, 0}, najv2 = {-inf, 0}; mx[v] = {0, 0};
for(auto u : g[v]){
if(u == p || visited[u])continue;
d[u] = d[v] + 1;
dfs2(u, v, dist);
if(mx[u].fi > najv1.fi){
najv2 = najv1;
najv1 = mx[u];
}
else if(mx[u].fi == najv1.fi)najv1.se += mx[u].se;
else if(mx[u].fi > najv2.fi){
najv2 = mx[u];
}else if(mx[u].fi == najv2.se)najv2.se += mx[u].se;
mx[v] = cmb(mx[v], mx[u]);
}
if(najv1.se > 1){
pll sad = {1ll * (dist + d[v]) * (2 * najv1.fi - 2 * d[v]), najv1.se * (najv1.se - 1) / 2};
rez = cmb(rez, sad);
}
else if(najv2.se > 0){
pll sad = {1ll * (dist + d[v]) * (najv1.fi + najv2.fi - 2 * d[v]), najv1.se * najv2.se};
rez = cmb(rez, sad);
}
}
int pref[mxN];
int sufi[mxN];
int main(){
cin.tie(0)->sync_with_stdio(0);
cin >> n;
ff(i,1,n - 1){
int u, v;
cin >> u >> v;
g[u].pb(v);
g[v].pb(u);
}
d[1] = 0; dfs1(1, -1); int a = -1; ff(i,1,n)if(a == -1 || d[a] < d[i])a = i;
d[a] = 0; dfs1(a, -1); int b = -1; ff(i,1,n)if(b == -1 || d[b] < d[i])b = i;
int dia = d[b];
vector<int> put;
for(int i = b; i != -1; i = par[i])put.pb(i);
for(auto c : put){
visited[c] = 1;
}
int len = sz(put);
ff(i,0,len - 1){
int v = put[i];
d[v] = 0; dfs2(v, -1, max(i, len - i - 1));
}
ff(i,0,len - 1){
int v = put[i];
pref[i] = (mx[v].fi == i ? mx[v].se : 0) + (i == 0 ? 0 : pref[i - 1]);
}
fb(i,len - 1,0){
int v = put[i];
sufi[i] = (mx[v].fi == len - i - 1 ? mx[v].se : 0) + (i == len - 1 ? 0 : sufi[i + 1]);
}
int najv = 0;
ff(i,0,len - 1){
int v = put[i];
najv = max(najv, mx[v].fi);
}
if(najv == 0){
cout << 0 << " " << 1 << '\n';
return 0;
}
rez = cmb(rez, make_pair(1ll * dia * najv, 1ll * pref[najv - 1] * sufi[len - najv]));
ff(i,najv,len - najv - 1){
int v = put[i];
if(mx[v].fi == 0)continue;
if(i <= len - i - 1){
ll distL = 1ll * (i + mx[v].fi) * (len - i - 1);
ll brL = 1ll * mx[v].se * pref[i - 1];
rez = cmb(rez, make_pair(distL, brL));
ll distR = 1ll * (len - i - 1 + mx[v].fi) * i;
ll brR = 1ll * mx[v].se * (len - i - 1 == i ? sufi[len - i] : sufi[len - i - 1]);
rez = cmb(rez, make_pair(distR, brR));
}
else{
ll distR = 1ll * (i + mx[v].fi) * (len - i - 1);
ll brR = 1ll * mx[v].se * pref[(len - i - 1) - 1];
rez = cmb(rez, make_pair(distR, brR));
ll distL = 1ll * (len - i - 1 + mx[v].fi) * i;
ll brL = 1ll * mx[v].se * sufi[i + 1];
rez = cmb(rez, make_pair(distL, brL));
}
}
cout << rez.fi << " " << rez.se << '\n';
return 0;
}
/*
7
1 2
1 3
2 4
2 5
3 6
3 7
4
1 2
2 3
2 4
5
1 2
2 3
3 4
4 5
// probati bojenje sahovski
*/
