Hard route

input/code.cpp: In function 'void h2(int, int)':
input/code.cpp:36:7: error: 't' was not declared in this scope
       t++, gp = *it;
       ^
input/code.cpp:36:7: note: suggested alternative: 'it'
       t++, gp = *it;
       ^
       it

#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
vector<int> v[500000];
vector<pair<int, int>> ov[500000];
long mv = 0, mc = 0;
pair<int, int> h1(int i, int p=-1) {
  ov[i].reserve(v[i].size());
  pair<int, int> trt{0, 1};
  for (int j : v[i]) {
    if (j == p) continue;
    auto cv = h1(j, i);
    ov[i].push_back(cv);
    if (cv.F > trt.F) trt = {cv.F, 0};
    if (cv.F == trt.F) trt.S += cv.S;
  }
  trt.F++;
  return trt;
}
void h2(int i, int p=-1) {
  map<int, int> am;
  auto &chv = ov[i];
  for (auto cv : chv) {
    am[cv.F] += cv.S;
  }
  if (v[i].size() == 1) am[0] = 1;
  int xi = 0;
  for (int j : v[i]) {
    if (j == p) continue;
    am[chv[xi].F] -= chv[xi].S;
    auto it = am.rbegin();
    pair<int, int> gp = *it;
    if (gp.S == 0) {
      if (am.size() == 1) exit(0);
      t++, gp = *it;
    }
    gp.F++;
    ov[j].push_back(gp);
    am[chv[xi].F] += chv[xi].S;
    h2(j, i);
    xi++;
  }
  if (v[i].size() == 1) return;
  map<int, int> uq;
  for (auto cv : chv) {
    uq[cv.F]++;
  }
  for (auto cv : chv) {
    am[cv.F] -= cv.S;
    if (am[cv.F] == 0) am.erase(cv.F);
    uq[cv.F]--;
    
    int opc = min(2, int(am.size()));
    int ops[2];
    auto it = am.rbegin();
    for (int cc = 0; cc < opc; ++cc, ++it) {
      ops[cc] = it->F;
    }
    for (int cc = 0; cc < opc; ++cc) {
      int co = ops[cc];
      uq[co]--;
      int sup = 0;
      for (int cc2 = 0; cc2 < opc; ++cc2) {
        if (uq[ops[cc2]]) sup = max(sup, ops[cc2]);
      }
      long rv = long(co+cv.F)*sup;
      if (rv > mv) mv = rv, mc = 0;
      if (rv == mv) mc += long(cv.S)*am[co];
      uq[co]++;
    }
    am[cv.F] += cv.S;
    uq[cv.F]++;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n-1; ++i) {
    int a, b;
    cin >> a >> b;
    a--; b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  h1(0);
  h2(0);
  if (mv == 0) mc = 2;
  cout << mv << " " << mc/2 << endl;
}