two paths

#include <bits/stdc++.h>
#define sz(x) ((int)(x).size())
#define endl '\n'
#define debug(X) cout << #X << " = " << X << endl
#define rep(i,a,b) for(int(i)=(a);(i)<(b);i++)
#define SZ(v) (int)v.size()

using namespace std;
typedef long long ll;
const int mod = (int) 1e9 + 7;
const int oo = (int) 1e9;

const int N = 1e5 + 2, E = 2e5 + 3;

int n, m, e;
int src, dst;
int head[N], nxt[E], to[E];

int longest_path[E][2], res[E];

/* fast input */
char buf[1<<24],*w=buf;
int getint(){
 while(!isdigit(*w))w++;
 int r = 0;
 while(isdigit(*w)){
   r = r * 10 + *w - '0';
   w++;
 }
 return r;
}

void init()
{
    e = 0;
    memset(head,-1,sizeof(head));
    memset(res,-1,sizeof(res));
}

void addEdge(int f, int t)
{
    nxt[e] = head[f];
    head[f] = e;
    to[e++] = t;
}

void addBiEdge(int a, int b)
{
    addEdge(a, b);
    addEdge(b, a);
}

int solve(int u, int p, int idx)
{
    if(~res[idx])return res[idx];
    int ans = 0;
    for(int k=head[u]; ~k; k=nxt[k]){
        int v = to[k];
        if(v==p) continue;
        int tmp = solve(v,u,k);
        longest_path[idx][0] = max(longest_path[idx][0], longest_path[k][1]+1);
        if(longest_path[idx][0] > longest_path[idx][1])
            swap(longest_path[idx][0], longest_path[idx][1]);
        ans = max(tmp, ans);
    }
    return res[idx] = max(ans, longest_path[idx][0] + longest_path[idx][1]);
}

int main()
{
    fread(buf,sizeof(char),1<<24,stdin);

    int n,a,b;
    int ans= 0;
    init();
    n = getint();
    pair<int,int> adj[N+1];
    int edge[E];
    rep(i,0,n-1)
    {
        a = getint();b = getint();
        edge[i]=e;
        addBiEdge(--a, --b);
        adj[i]= make_pair(a,b);
    }
    rep(i,0,n-1)
    {
        a = adj[i].first; b = adj[i].second;
        solve(a, b, edge[i]+1);
        solve(b, a, edge[i]);
    }
    rep(i,0,n-1)
        ans=max(ans, res[edge[i]]*res[edge[i]+1]);
    printf("%d", ans);
    return 0;
}