#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
set<int> adjl[2005];
int sz[2005];
bool block[2005];
bool done[2005];
int n;
void dfs(int node, int p){
sz[node] = 1;
for (int x : adjl[node]){
if (x==p) continue;
if (block[x]) continue;
dfs(x,node);
sz[node] += sz[x];
}
}
int findCentroid(int node, int p, int total){
for (int x : adjl[node]){
if (x==p) continue;
if (block[x]) continue;
if (sz[x]>total/2){
return findCentroid(x,node,total);
}
}
return node;
}
void addNode(int node, int root){
dfs(root,-1);
if (sz[root]==1){
adjl[root].insert(node);
adjl[node].insert(root);
return;
}
if (sz[root]==2){
int ch = -1;
for (int x : adjl[root]){
if (block[x]) continue;
ch = x;
}
int res = Query(root,ch,node);
if (res==root){
adjl[root].insert(node);
adjl[node].insert(root);
}
else if (res==ch){
adjl[ch].insert(node);
adjl[node].insert(ch);
}
else if (res==node){
adjl[root].erase(ch);
adjl[ch].erase(root);
adjl[root].insert(node);
adjl[node].insert(root);
adjl[ch].insert(node);
adjl[node].insert(ch);
}
else{
adjl[root].erase(ch);
adjl[ch].erase(root);
adjl[root].insert(res);
adjl[res].insert(root);
adjl[ch].insert(res);
adjl[res].insert(ch);
adjl[res].insert(node);
adjl[node].insert(res);
done[res] = true;
}
return;
}
root = findCentroid(root,-1,sz[root]);
dfs(root,-1); ///re-root at centroid
//printf("centroid %d\n",root);
vector<pair<int,int> > children;
for (int child : adjl[root]){
if (block[child]) continue;
children.push_back({sz[child],child});
//printf("added %d %d\n",sz[child],child);
}
sort(children.begin(),children.end(),greater<pair<int,int> >());
//assert(children.size()!=1);
if (children.size()&1){
children.push_back(children[0]);
}
for (int x = 0; x<children.size(); x+=2){
int n1 = children[x].second;
int n2 = children[x+1].second;
int res = Query(node,n1,n2);
if (res==n1){
block[root] = true;
addNode(node,n1);
block[root] = false;
return;
}
if (res==n2){
block[root] = true;
addNode(node,n2);
block[root] = false;
return;
}
if (res!=root){
///res is either on edge root-n1 or root-n2
int res2 = Query(root,n1,res);
if (res2==res){
adjl[root].erase(n1);
adjl[n1].erase(root);
adjl[root].insert(res);
adjl[n1].insert(res);
adjl[res].insert(root);
adjl[res].insert(n1);
if (res!=node){
adjl[res].insert(node);
adjl[node].insert(res);
}
}
else if (res2==root){
adjl[root].erase(n2);
adjl[n2].erase(root);
adjl[root].insert(res);
adjl[n2].insert(res);
adjl[res].insert(root);
adjl[res].insert(n2);
if (res!=node){
adjl[node].insert(res);
adjl[res].insert(node);
}
}
else{
//assert(false);
}
done[res] = true;
return;
}
}
///directly connected to root
adjl[root].insert(node);
adjl[node].insert(root);
}
void Solve(int N) {
n = N;
for (int nw = 1; nw<N; nw++){
if (done[nw]) continue;
addNode(nw,0);
/*for (int x = 0; x<N; x++){
for (int node : adjl[x]){
if (node<=x){
//printf("now %d, %d--%d\n",nw,node,x);
}
}
}*/
}
for (int x = 0; x<N; x++){
for (int node : adjl[x]){
if (node<x){
Bridge(node,x);
}
}
}
}
