#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define eb emplace_back
#define pu push
#define ins insert
#define fi first
#define se second
#define all(a) a.begin(),a.end()
#define bruh ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fu(x,a,b) for (auto x=a;x<=b;x++)
#define fd(x,a,b) for (auto x=a;x>=b;x--)
#define int ll
using namespace std;
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
/*
Competitive Programming notes that I need to study & fix my dumbass self:
1. Coding:
- Always be sure to check the memory of arrays (maybe use vectors), for loops
- Always try to maximize the memory if possible, even if you are going for subtasks
- Do not exploit #define int long long, it will kill you
2. Stress:
- Always try generating big testcases and try if they run
3. Time management:
- Don't overcommit or undercommit, always spend a certain amount of time to think a problem, don't just look at it and say I'm fucked
- Do not spend too much time coding brute-force solutions, they should be easily-codable solutions that don't take up too much time
Time management schedule:
Offline / LAH days (4 problems - 3h):
15' thinking of solution / idea
1. no idea: skip
2. yes idea: continue thinking for <= 15'
+ implementing: <= 20'
+ brute-force: <= 5'
+ test generator: <= 5'
I hate offline because I am dumb
*/
typedef pair<int, int> ii;
const int N = 5e5+5;
const int B = 750;
const int mod = 1e9+7;
const int inf = 1e18;
using cd = complex<double>;
const long double PI = acos(-1);
int power(int a,int b) {ll x = 1;if (a >= mod) a%=mod; while (b) {if (b & 1) x = x*a % mod;a = a*a % mod;b>>=1;}return x;}
int n;
vector<int> adj[N];
int tin[N], tout[N], timer = 0, rev[N];
int dist[N], depth[N], cnt[N];
int ans = 0, cres = 1;
ii st[4*N];
int lazy[4*N];
ii merge(ii a, ii b)
{
if (a.fi == b.fi) return {a.fi, a.se+b.se};
return max(a, b);
}
void push(int id)
{
st[id*2].fi += lazy[id]; st[id*2+1].fi += lazy[id];
lazy[id*2] += lazy[id], lazy[id*2+1] += lazy[id];
lazy[id] = 0;
}
void build(int id, int l, int r)
{
if (l == r)
{
st[id] = {dist[rev[l]], 1};
return;
}
int mid = l+r>>1;
build(id*2, l, mid), build(id*2+1, mid+1, r);
st[id] = merge(st[id*2], st[id*2+1]);
}
void update(int id, int l, int r, int u, int v, int val)
{
if (v < u) return;
if (l > v || r < u) return;
if (u <= l && r <= v)
{
st[id].fi += val;
lazy[id] += val;
return;
}
push(id);
int mid = l+r>>1;
update(id*2, l, mid, u, v, val); update(id*2+1, mid+1, r, u, v, val);
st[id] = merge(st[id*2], st[id*2+1]);
}
ii get(int id, int l, int r, int u, int v)
{
if (v < u) return {0, 0};
if (l > v || r < u) return {0, 0};
if (u <= l && r <= v) return st[id];
push(id);
int mid = l+r>>1;
return merge(get(id*2, l, mid, u, v), get(id*2+1, mid+1, r, u, v));
}
void predfs(int u, int p)
{
depth[u] = 0, cnt[u] = 1;
tin[u] = ++timer;
rev[timer] = u;
for (auto v : adj[u])
{
if (v == p) continue;
dist[v] = dist[u] + 1;
predfs(v, u);
if (depth[v]+1 > depth[u]) depth[u] = depth[v]+1, cnt[u] = cnt[v];
else if (depth[v]+1 == depth[u]) cnt[u] += cnt[v];
}
tout[u] = timer;
}
void dfs(int u, int p)
{
if (adj[u].size() == 1) return;
// cout<<u<<endl;
// for (int i = 1; i <= n; i++) cout<<get(1,1,n,tin[i],tin[i]).fi<<" ";
// cout<<endl;
ii m1 = {-1, -1}, m2 = {-1, -1}, m3 = {-1, -1};
vector<ii> a;
if (p)
{
a.pb(merge(get(1, 1, n, 1, tin[u]-1), get(1, 1, n, tout[u]+1, n)));
m1 = a.back();
}
for (auto v : adj[u])
{
if (v == p) continue;
ii cur = {depth[v]+1, cnt[v]};
if (cur > m1) m3 = m2, m2 = m1, m1 = cur;
else if (cur > m2) m3 = m2, m2 = cur;
else if (cur > m3) m3 = cur;
a.pb(cur);
}
int c12 = 0, c23 = 0, c13 = 0, c1 = 0, c2 = 0, c3 = 0;
// cout<<u<<endl;
for (auto i : a)
{
// cout<<i.fi<<" "<<i.se<<" "<<c1<<" "<<c2<<" "<<c3<<endl;
if (m1.fi == m2.fi && i.fi == m1.fi) c12 += i.se * c1;
if (m1.fi == m3.fi && i.fi == m1.fi) c13 += i.se * c1;
if (m2.fi == m3.fi && i.fi == m2.fi) c23 += i.se * c2;
if (i.fi == m1.fi) c1 += i.se;
if (i.fi == m2.fi) c2 += i.se;
if (i.fi == m3.fi) c3 += i.se;
}
// cout<<c23<<endl;
if (m1.fi != m2.fi) c12 = c1 * c2;
if (m1.fi != m3.fi) c13 = c1 * c3;
if (m2.fi != m3.fi) c23 = c2 * c3;
// cout<<u<<" "<<m1.fi<<" "<<m2.fi<<" "<<m3.fi<<" "<<c12<<" "<<c13<<" "<<c23<<endl;
if (m3.fi != -1)
{
int val = m1.fi * (m2.fi + m3.fi);
if (val > ans)
{
ans = val;
cres = c23;
} else if (val == ans)
{
cres += c23;
}
}
for (auto v : adj[u])
{
if (v == p) continue;
update(1, 1, n, 1, tin[v]-1, 1); update(1, 1, n, tout[v]+1, n, 1);
update(1, 1, n, tin[v], tout[v], -1);
dfs(v, u);
update(1, 1, n, tin[v], tout[v], 1);
update(1, 1, n, 1, tin[v]-1, -1); update(1, 1, n, tout[v]+1, n, -1);
}
}
void solve()
{
cin>>n;
for (int i = 1; i < n; i++)
{
int u,v; cin>>u>>v;
adj[u].pb(v); adj[v].pb(u);
}
if (n == 2)
{
cout<<"0 1"; return;
}
int root = 1, l = 0;
for (int i = 1; i <= n; i++)
{
if (adj[i].size() > 1) root = i;
else l++;
}
predfs(root, 0);
// for (int i = 1; i <= n; i++) cout<<dist[i]<<" ";
// cout<<endl;
build(1,1,n);
// for (int i = 1; i <= n; i++) cout<<depth[i]<<" "<<cnt[i]<<endl;
dfs(root, 0);
cout<<ans<<" "<<cres;
}
/*
Go through the mistakes you usually make and revise your code, for god's sake...
*/
signed main()
{
bruh
//freopen("input.inp","r",stdin);
//freopen("output.inp","w",stdout);
int t = 1;
// cin>>t;
while (t--)
{
solve();
cout<<"\n";
}
}
