#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define pii pair<ll,ll>
#define f first
#define s second
#define chmin(a, b) a = min(a,b)
#define chmax(a, b) a = max(a,b)
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define all(x) x.begin(),x.end()
#define vec vector
const int MAX_N = 5e5;
vec<int> adj[MAX_N];
vec<pii> paths[MAX_N];
vec<ll> path[MAX_N];
pii mxpath[MAX_N];
pii ans = {0,1};
void dfs(int cur, int par=-1) {
mxpath[cur] = {0,0};
for (int x : adj[cur]) {
if (x!=par) {
dfs(x,cur);
paths[cur].pb({mxpath[x].f+1,mxpath[x].s});
chmax(mxpath[cur].f,mxpath[x].f+1);
}
}
for (auto[x,w] : paths[cur]) {
if (x!=mxpath[cur].f) {continue;}
mxpath[cur].s += w;
}
if (adj[cur].size()==1) {paths[cur] = {mxpath[cur] = {0,1}};}
}
void dfs2(int cur, int par=-1, pii par_info = {-1,1}) {
paths[cur].pb({par_info.f+1,par_info.s});
sort(all(paths[cur]),greater<>());
path[cur] = {paths[cur][0].s};
vec<ll> squares = {paths[cur][0].s*paths[cur][0].s};
for (int i=1;i<paths[cur].size();i++) {
if (paths[cur][i].f!=paths[cur][i-1].f) {path[cur].pb(0); squares.pb(0);}
path[cur].back() += paths[cur][i].s;
squares.back() += (paths[cur][i].s*paths[cur][i].s);
}
if (adj[cur].size()>=3) {
pii best;
ll mx[3] = {paths[cur][0].f,paths[cur][1].f,paths[cur][2].f};
//cout << cur+1 << ' ' << squares[1]<<' '<<path[cur][1]<<'\n';
//cout << cur+1 << ' ' << mx[0]<<' '<<mx[1]<<' '<<mx[2]<<'\n';
best.f = (mx[1]+mx[2])*mx[0];
if (mx[0]!=mx[1] && mx[1]!=mx[2]) {
best.s = path[cur][1]*path[cur][2];
} else if (mx[0]==mx[1] && mx[1]!=mx[2]) {
best.s = path[cur][0]*path[cur][1];
} else if (mx[0]!=mx[1] && mx[1]==mx[2]) {
best.s = (path[cur][1]*path[cur][1]-squares[1])/2;
} else {
best.s = (path[cur][0]*path[cur][0]-squares[0])/2;
}
if (ans.f==best.f) {ans.s += best.s;}
else if (best.f>ans.f) {ans = best;}
}
for (int x : adj[cur]) {
if (x!=par) {
if (mxpath[x].f+1==paths[cur][0].f) {
if (mxpath[x].s==path[cur][0]) {
dfs2(x,cur,{paths[cur][1].f,path[cur][1]});
} else {
dfs2(x,cur,{paths[cur][0].f,path[cur][0]-mxpath[x].s});
}
} else {
dfs2(x,cur,{paths[cur][0].f,path[cur][0]});
}
}
}
}
int main() {
ios::sync_with_stdio(false); cin.tie(0);
int n; cin >> n;
for (int i=0;i<n-1;i++) {
int a, b; cin >> a >> b;
adj[--a].pb(--b);
adj[b].pb(a);
}
int rt = 0;
for (int i=0;i<n;i++) {if (adj[i].size()>1) {rt = i;}}
dfs(rt);
dfs2(rt);
cout << ans.f << ' ' << ans.s << '\n';
}
