#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin >> n;
vector<vector<int>> con(n);
for(int i = 0; i < n-1; i++) {
int a, b;
cin >> a >> b;
a--; b--;
con[a].push_back(b);
con[b].push_back(a);
}
vector<ll> d(n);
function<void(int, int)> dfs = [&](int curr, int prev) {
for(int next : con[curr]) {
if(next == prev)
continue;
dfs(next, curr);
d[curr] = max(d[curr], d[next]+1);
}
};
dfs(0, -1);
ll best = 0, cnt = 1;
auto updateBest = [&](ll v, ll ways) {
if(v > best) {
best = v;
cnt = ways;
}
else if(v == best) {
cnt += ways;
}
};
function<void(int, int, ll)> reroot = [&](int curr, int prev, ll parDist) {
map<ll, ll> dists;
dists[parDist]++;
for(int next : con[curr]) {
if(next == prev)
continue;
dists[d[next]+1]++;
}
//4 cases
//Let A>B>C be the furthest distances from this node
//We look at the counts of each
//A B C
//3
//2 x
//1 x
//1 1 x
if(sz(con[curr]) >= 3) {
auto it = dists.rbegin();
auto [A, cnt1] = *it;
ll v, ways;
//3
if(cnt1 >= 3) {
v = (A+A)*A;
ways = cnt1*(cnt1-1)/2;
}
else {
it++;
auto [B, cnt2] = *it;
if(cnt1+cnt2 >= 3) {
//2 x
if(cnt1 == 2) {
v = (A+B)*A;
ways = cnt1*cnt2;
}
//1 x
else {
v = (B+B)*A;
ways = cnt2*(cnt2-1)/2;
}
}
else {
it++;
auto [C, cnt3] = *it;
assert(cnt1 == 1 && cnt2 == 1);
v = (B+C)*A;
ways = cnt3;
}
}
updateBest(v, ways);
}
for(int next : con[curr]) {
if(next == prev)
continue;
auto it = dists.rbegin();
if(it->second == 1 && d[next]+1 == it->first) {
it--;
reroot(next, curr, it->first+1);
it++;
}
else {
reroot(next, curr, it->first+1);
}
}
};
reroot(0, -1, 0);
cout << best << " " << cnt << "\n";
}
