#include <bits/stdc++.h>
const int maxn = 5e5 + 5;
long long mx_len, ways;
int N, x, y, z;
std::vector<int> G[maxn + 5];
std::pair<int, int> f[maxn + 5][3];
int cnt[maxn + 5][3];
void preDFS(int u, int p) {
int &cnt1 = cnt[u][0], &cnt2 = cnt[u][1], &cnt3 = cnt[u][2];
std::pair<int, int> &pf = f[u][0], &ps = f[u][1], &pt = f[u][2];
if (p && G[u].size() == 1) {
cnt1 = 1;
pf = {0, 1};
return;
}
for (int v : G[u]) {
if (v == p) continue;
preDFS(v, u);
std::tie(x, y) = f[v][0];
x++;
if (x > pf.first) {
std::swap(cnt1, cnt2);
ps = pf;
cnt1 = 1;
pf = {x, y};
} else if (x == pf.first) {
cnt1++;
pf.second += y;
} else if (x > ps.first) {
std::swap(cnt2, cnt3);
pt = ps;
cnt2 = 1;
ps = {x, y};
} else if (x == ps.first) {
cnt2++;
ps.second += y;
} else if (x > pt.first) {
cnt3 = 1;
pt = {x, y};
} else if (x == pt.first) {
cnt3++;
pt.second += y;
}
}
}
void DFS(int u, int p, std::pair<int, int> tmp) {
int cnt1 = cnt[u][0], cnt2 = cnt[u][1], cnt3 = cnt[u][2];
std::pair<int, int> pf = f[u][0], ps = f[u][1], pt = f[u][2];
std::tie(x, y) = tmp;
x++;
if (x > pf.first) {
std::swap(cnt1, cnt2);
ps = pf;
cnt1 = 1;
pf = {x, y};
} else if (x == pf.first) {
cnt1++;
pf.second += y;
} else if (x > ps.first) {
std::swap(cnt2, cnt3);
pt = ps;
cnt2 = 1;
ps = {x, y};
} else if (x == ps.first) {
cnt2++;
ps.second += y;
} else if (x > pt.first) {
cnt3 = 1;
pt = {x, y};
} else if (x == pt.first) {
cnt3++;
pt.second += y;
}
// if (u == 2) {
// std::cout << "? " << cnt1 << ' ' << cnt2 << ' ' << cnt3 << ' ' << pf.second << ' ' << f[u][0].second << '\n';
// }
if (cnt1 >= 3) {
x = pf.first;
long long len = 1ll * (x + x) * x, num = 0;
for (int v : G[u]) {
if (v == p) continue;
std::tie(x, y) = f[v][0];
x++;
if (x == pf.first) {
num += 1ll * y * (pf.second - y);
}
}
if (tmp.first + 1 == pf.first) {
num += 1ll * tmp.second * (pf.second - tmp.second);
}
if (len > mx_len) {
mx_len = len;
ways = num;
} else if (len == mx_len) {
ways += num;
}
} else if (cnt2 >= 2) {
// x > y
x = pf.first;
y = ps.first;
long long len = 1ll * (y + y) * x, num = 0;
for (int v : G[u]) {
if (v == p) continue;
std::tie(x, y) = f[v][0];
x++;
if (x == ps.first) {
num += 1ll * y * (ps.second - y);
}
}
if (tmp.first + 1 == ps.first) {
num += 1ll * tmp.second * (ps.second - tmp.second);
}
if (len > mx_len) {
mx_len = len;
ways = num;
} else if (len == mx_len) {
ways += num;
}
// (y + y) * x = x * y + x * y;
// (x + y) * y = y * y + x * y (max)
} else if (cnt3) {
// x > y > z
x = pf.first;
y = ps.first;
z = pt.first;
long long len = 1ll * (y + z) * x, num = 1ll * pt.second * ps.second;
if (len > mx_len) {
mx_len = len;
ways = num;
} else if (len == mx_len) {
ways += num;
}
// (x + y) * z = x * z + y * z;
// (x + z) * y = x * y + y * z;
// (y + z) * x = x * y + x * z; (max)
}
std::vector<std::pair<int, int>> pref, suff;
pref.push_back({0, 0});
suff.push_back({0, 0});
for (int v : G[u]) {
if (v == p) continue;
std::tie(x, y) = f[v][0];
x++;
if (pref.back().first < x) {
pref.push_back({x, y});
} else if (pref.back().first == x) {
pref.push_back({x, pref.back().second + y});
} else {
pref.push_back(pref.back());
}
}
for (int i = G[u].size() - 1; i >= 0; --i) {
int v = G[u][i];
if (v == p) continue;
std::tie(x, y) = f[v][0];
x++;
if (suff.back().first < x) {
suff.push_back({x, y});
} else if (suff.back().first == x) {
suff.push_back({x, suff.back().second + y});
} else {
suff.push_back(suff.back());
}
}
std::pair<int, int> otmp;
for (int i = 0; i < G[u].size(); ++i) {
int v = G[u][i];
if (v == p) continue;
otmp = tmp;
std::tie(x, y) = pref[i];
if (x > tmp.first) {
tmp = {x, y};
} else if (x == tmp.first) {
tmp.second += y;
}
std::tie(x, y) = suff[G[u].size() - 1 - i];
if (x > tmp.first) {
tmp = {x, y};
} else if (x == tmp.first) {
tmp.second += y;
}
DFS(v, u, tmp);
tmp = otmp;
}
}
int main() {
std::cin.tie(0)->sync_with_stdio(0);
std::cin >> N;
for (int i = 1; i < N; ++i) {
int u, v; std::cin >> u >> v;
G[u].push_back(v);
G[v].push_back(u);
}
preDFS(1, 0);
DFS(1, 0, {0, 1});
if (!mx_len) {
std::cout << 0 << ' ' << 1 << '\n';
} else {
std::cout << mx_len << ' ' << ways / 2 << '\n';
}
return 0;
}
