#include <iostream>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <ctime>
#include <sstream>
#include <algorithm>
#include <functional>
#include <numeric>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
using namespace std;
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define ll long long
#define pii pair < int, int >
#define pll pair < long long, long long>
#define ull unsigned long long
#define y1 stupid_cmath
#define left stupid_left
#define right stupid_right
#define vi vector <int>
#define sz(a) (int)a.size()
#define forit(it, s) for(__typeof(s.begin()) it = s.begin(); it != s.end(); it++)
#define all(a) a.begin(), a.end()
#define sqr(x) ((x) * (x))
const int inf = (int)1e9;
const int mod = inf + 7;
const double eps = 1e-9;
const double pi = acos(-1.0);
inline void read(int &x)
{
char c = '0'; c--;
x = 0;
while((c < '0' || c > '9')) c = getchar();
while((c >= '0' && c <= '9')) x = x * 10 + c - '0', c = getchar();
}
int n;
vector<int> g[1001000];
pii up[1001000], dp[1001000];
ll best = -inf, ans = -inf;
vector<int> goods;
void update(pii &a, int x, int y) {
if (x < 0) return;
if (x > a.f) a = mp(x, y);
else if (x == a.f) a.s += y;
}
void calc_dp(int v, int par) {
dp[v] = mp(0, 1);
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
calc_dp(to, v);
update(dp[v], dp[to].f + 1, dp[to].s);
}
}
void calc_up(int v, int par) {
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
up[to] = mp(0, 1);
update(up[to], up[v].f + 1, up[v].s);
}
pii cur = mp(-inf, -inf);
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
update(up[to], cur.f + 2, cur.s);
update(cur, dp[to].f, dp[to].s);
}
reverse(all(g[v]));
cur = mp(-inf, -inf);
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
update(up[to], cur.f + 2, cur.s);
update(cur, dp[to].f, dp[to].s);
}
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
calc_up(to, v);
}
}
int get_cnt(int v, int par, ll val) {
int res = 0;
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
if (dp[to].f + 1 == val) res += dp[to].s;
}
return res;
}
ll calc_sum_of_pairwise_sum(int v, int par, ll val) {
ll res2 = 0, res1 = 0;
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
if (dp[to].f + 1 == val) {
res2 += dp[to].s * 1ll * dp[to].s;
res1 += dp[to].s;
}
}
return (res1 * res1 - res2) / 2;
}
void update(pii &a, pii &b, pii &c, int x, int y) {
if (x > a.f) {
c = b;
b = a;
a = mp(x, y);
} else if (x > b.f) {
c = b;
b = mp(x, y);
} else if (x > c.f) {
c = mp(x, y);
}
}
void calc_ans(int v, int par) {
pii data1 = mp(-inf, -inf);
pii data2 = mp(-inf, -inf);
pii data3 = mp(-inf, -inf);
if (par != -1) update(data1, data2, data3, up[v].f, up[v].s);
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
update(data1, data2, data3, dp[to].f + 1, dp[to].s);
}
if (data3.f != -inf) {
int mx3 = data3.f, cnt3 = data3.s;
int mx2 = data2.f, cnt2 = data2.s;
int mx1 = data1.f, cnt1 = data1.s;
ll val = (mx2 + mx3) * 1ll * mx1;
if (val > best) {
best = val;
goods.clear();
goods.pb(v);
} else if (val == best) {
goods.pb(v);
}
}
forit (it, g[v]) {
int to = *it;
if (to == par) continue;
calc_ans(to, v);
}
}
void process(int root) {
int par = -1;
calc_dp(root, -1);
pii data1 = mp(-inf, -inf);
pii data2 = mp(-inf, -inf);
pii data3 = mp(-inf, -inf);
forit (it, g[root]) {
int to = *it;
if (to == par) continue;
update(data1, data2, data3, dp[to].f + 1, dp[to].s);
}
int mx3 = data3.f, cnt3 = data3.s;
int mx2 = data2.f, cnt2 = data2.s;
int mx1 = data1.f, cnt1 = data1.s;
ll res = 0;
if (mx1 != mx2 && mx2 != mx3) {
cnt3 = get_cnt(root, par, mx3);
res = cnt2 * cnt3;
} else if (mx1 != mx2 && mx2 == mx3) {
res = calc_sum_of_pairwise_sum(root, par, mx3);
} else if (mx1 == mx2 && mx2 != mx3) {
cnt3 = get_cnt(root, par, mx3);
res = (cnt1 + cnt2) * cnt3;
} else if (mx1 == mx2 && mx2 == mx3) {
res = calc_sum_of_pairwise_sum(root, par, mx3);
} else {
assert(false);
}
ans += res;
}
int main(){
read(n);
for (int i = 0, x, y; i < n - 1; i++) {
read(x);
read(y);
x--; y--;
g[x].pb(y);
g[y].pb(x);
}
int leaf_number = 0;
for (int i = 0; i < n; i++) {
if (g[i].size() == 1) leaf_number++;
}
if (leaf_number == 2) {
printf("0 1\n");
return 0;
}
calc_dp(0, -1);
up[0] = mp(0, 1);
calc_up(0, -1);
calc_ans(0, -1);
ans = 0;
for (int i = 0; i < goods.size(); i++) {
process(goods[i]);
}
printf("%lld %lld\n", best, ans);
return 0;
}
