#include <bits/stdc++.h>
using i64 = long long;
#ifdef DEBUG
#include "/home/ahmetalp/Desktop/Workplace/debug.h"
#else
#define debug(...) void(23)
#endif
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int N;
std::cin >> N;
std::vector<std::vector<int>> adj(N);
for (int i = 1; i < N; ++i) {
int A, B;
std::cin >> A >> B;
--A, --B;
adj[A].emplace_back(B);
adj[B].emplace_back(A);
}
std::vector<int> h(N), cnt(N, 1);
auto dfs1 = [&](auto&& self, int v, int pr) -> void {
for (auto u : adj[v]) {
if (u == pr) {
continue;
}
self(self, u, v);
if (h[u] + 1 > h[v]) {
h[v] = h[u] + 1;
cnt[v] = cnt[u];
} else if (h[u] + 1 == h[v]) {
cnt[v] += cnt[u];
}
}
};
dfs1(dfs1, 0, 0);
i64 ansval = 0, anscpth = 1;
auto dfs2 = [&](auto&& self, int v, int pr, int hpr, int cntpr) -> void {
std::vector<std::array<int, 2>> paths;
if (v > 0 || adj[v].size() == 1) {
paths.push_back({hpr, cntpr});
}
for (auto u : adj[v]) {
if (u == pr) {
continue;
}
paths.push_back({h[u] + 1, cnt[u]});
}
if (adj[v].size() >= 3) {
std::sort(paths.begin(), paths.end(), std::greater());
debug(v, paths);
i64 a = paths[0][0];
i64 b = paths[1][0];
i64 c = paths[2][0];
i64 val = a * (b + c);
i64 cpth = 0;
i64 tie = 0;
for (auto[x, y] : paths) {
if (x == c) {
tie += y;
}
}
if (a == b && b == c) {
cpth = tie * tie;
for (auto[x, y] : paths) {
if (x == c) {
cpth -= y * y;
}
}
cpth /= 2;
} else if (a == b) {
cpth = (paths[0][1] + paths[1][1]) * tie;
} else if (b == c) {
cpth = tie * tie;
for (auto[x, y] : paths) {
if (x == c) {
cpth -= y * y;
}
}
cpth /= 2;
} else {
cpth = paths[1][1] * tie;
}
if (val > ansval) {
ansval = val;
anscpth = cpth;
} else if (val == ansval) {
anscpth += cpth;
}
}
int longest1 = -1, longest2 = -1;
int cntlong1 = 0, cntlong2 = 0;
for (auto[x, y] : paths) {
x++;
if (x > longest1) {
longest2 = longest1;
cntlong2 = cntlong1;
longest1 = x;
cntlong1 = y;
} else if (x == longest1) {
cntlong1 += y;
} else if (x > longest2) {
longest2 = x;
cntlong2 = y;
} else if (x == longest2) {
cntlong2 += y;
}
}
for (auto u : adj[v]) {
if (u == pr) {
continue;
}
if (h[u] + 2 == longest1) {
if (cnt[u] == cntlong1) {
self(self, u, v, longest2, cntlong2);
} else {
self(self, u, v, longest1, cntlong1 - cnt[u]);
}
} else {
self(self, u, v, longest1, cntlong1);
}
}
};
dfs2(dfs2, 0, 0, 0, 1);
std::cout << ansval << ' ' << anscpth << '\n';
return 0;
}
