This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/assoc_container.hpp>
#define fi first
#define se second
#define pb push_back
#define sz(c) (int)(c).size()
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define in freopen("road.in", "r", stdin);
#define out freopen("road.out", "w", stdout);
using namespace std;
using namespace __gnu_pbds;
#pragma GCC optimize("Ofast")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,popcnt,abm,mmx,tune=native")
#pragma GCC optimize("fast-math")
#pragma warning(disable : 4996)
typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
const int N = 5005;
const int INF = INT_MAX;
const int MOD = 998244353;
int TN = 1;
int n;
vector<int> leafs;
vector<int> verr[N];
int d[N][N], parent[N][N];
int get(int x, int y) {
    set<int> path; multiset<int> mpath;
    // printf("%d %d %d\n", x, y, parent[x][y]);
    // printf("cities between %d & %d are: ", x, y);
    while (parent[x][y] != 0) {
        path.insert(y); mpath.insert(y);
        y = parent[x][y];
    }
    path.insert(x); mpath.insert(x);
    if (sz(path) != sz(mpath)) {
        return -INF;
    }
    /*for (auto i: path) {
        printf("%d ", i);
    }
    puts("");*/
    int cur_ans = 0;
    for (int i = 1; i <= n; i++) {
        if (path.find(i) == path.end()) {
            // printf("%d ", i);
            int cur = INF;
            for (auto j: path) {
                // printf("%d %d ", j, d[i][j]);
                cur = min(cur, d[i][j]);
            }
            // puts("");
            cur_ans = max(cur_ans, cur);
        }
    }
    return cur_ans;
}
void solve() {
    scanf("%d", &n);
    for (int i = 1; i < n; i++) {
        int x, y;
        scanf("%d %d", &x, &y);
        verr[x].pb(y); verr[y].pb(x);
    }
    for (int i = 1; i <= n; i++) {
        if (sz(verr[i]) == 1) {
            leafs.pb(i);
        }
    }
    for (int i = 1; i <= n; i++) {
        queue<int> q; d[i][i] = 0; q.push(i); parent[i][i] = 0;
        while (!q.empty()) {
            int x = q.front(); q.pop();
            for (auto to: verr[x]) {
                if (!d[i][to] && to != i) {
                    d[i][to] = d[i][x] + 1;
                    parent[i][to] = x; q.push(to);
                }
            }
        }
    }
    int ans = 0, cnt = 0;
    for (int i = 0; i < sz(leafs); i++) {
        for (int j = i + 1; j < sz(leafs); j++) {
            // puts("");
            int len = d[leafs[i]][leafs[j]], H = get(leafs[i], leafs[j]);
            // printf("%d %d %d %d \n", leafs[i], leafs[j], len, H);
            // puts("");
            len *= H;
            if (ans < len) {
                ans = len, cnt = 1;
            }
            else if (ans == len) {
                cnt++;
            }
        }
    }
    printf("%d %d", ans, cnt);
    return;
}
signed main() {
    // ios_base::sync_with_stdio(0);
    // in; out; // cin >> TN;
    while (TN--) { solve(); }
    return 0;
 }
Compilation message (stderr)
road.cpp:22:0: warning: ignoring #pragma warning  [-Wunknown-pragmas]
 #pragma warning(disable : 4996)
 
road.cpp: In function 'void solve()':
road.cpp:70:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d", &n);
     ~~~~~^~~~~~~~~~
road.cpp:73:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%d %d", &x, &y);
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