#define DEBUG 0
#include <bits/stdc++.h>
using namespace std;
#if DEBUG
// basic debugging macros
int __i__,__j__;
#define printLine(l) for(__i__=0;__i__<l;__i__++){cout<<"-";}cout<<endl
#define printLine2(l,c) for(__i__=0;__i__<l;__i__++){cout<<c;}cout<<endl
#define printVar(n) cout<<#n<<": "<<n<<endl
#define printArr(a,l) cout<<#a<<": ";for(__i__=0;__i__<l;__i__++){cout<<a[__i__]<<" ";}cout<<endl
#define print2dArr(a,r,c) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<a[__i__][__j__]<<" ";}cout<<endl;}
#define print2dArr2(a,r,c,l) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<setw(l)<<setfill(' ')<<a[__i__][__j__]<<" ";}cout<<endl;}
// advanced debugging class
// debug 1,2,'A',"test";
class _Debug {
public:
template<typename T>
_Debug& operator,(T val) {
cout << val << endl;
return *this;
}
};
#define debug _Debug(),
#else
#define printLine(l)
#define printLine2(l,c)
#define printVar(n)
#define printArr(a,l)
#define print2dArr(a,r,c)
#define print2dArr2(a,r,c,l)
#define debug
#endif
// define
#define MAX_VAL 999999999
#define MAX_VAL_2 999999999999999999LL
#define EPS 1e-6
#define mp make_pair
#define pb push_back
// typedef
typedef unsigned int UI;
typedef long long int LLI;
typedef unsigned long long int ULLI;
typedef unsigned short int US;
typedef pair<int,int> pii;
typedef pair<LLI,LLI> plli;
typedef vector<int> vi;
typedef vector<LLI> vlli;
typedef vector<pii> vpii;
typedef vector<plli> vplli;
// ---------- END OF TEMPLATE ----------
#include "meetings.h"
int M[2000][2000];
int lca(int v,int w) {
if ((v == 0) || (w == 0)) return 0;
else if (v == w) return v;
if (M[v][w] != -1) return M[v][w];
else {
M[v][w] = M[w][v] = Query(0,v,w);
return M[v][w];
}
}
vi adjList[2000];
int done[2000];
int parent[2000],size[2000],heavy[2000];
int chain[2000],head[2000],csize[2000],tail[2000],c = 0;
int doDFS(int u,int p) {
int i;
parent[u] = p,size[u] = 1,heavy[u] = -1;
for (i = 0; i < adjList[u].size(); i++) {
int v = adjList[u][i];
if (v != p) {
size[u] += doDFS(v,u);
if ((heavy[u] == -1) || (size[v] > size[heavy[u]])) heavy[u] = v;
}
}
return size[u];
}
int doHLD(int u,int p) {
int i;
chain[u] = c,tail[c] = u;
if (csize[c] == 0) head[c] = u;
csize[c]++;
if (heavy[u] != -1) doHLD(heavy[u],u);
for (i = 0; i < adjList[u].size(); i++) {
int v = adjList[u][i];
if ((v != p) && (v != heavy[u])) c++,doHLD(v,u);
}
return 0;
}
int add(int u,int s) {
int i;
if (heavy[s] == -1) {
adjList[s].pb(u);
adjList[u].pb(s);
return 0;
}
int x = tail[chain[s]];
int v = lca(x,u);
if (!done[v]) {
vi path;
int t = s;
while (t != -1) path.pb(t),t = heavy[t];
int l = 1,r = path.size()-1;
while (l < r) {
int m = (l+r) / 2;
if (lca(path[m],u) == v) r = m;
else l = m+1;
}
adjList[path[l-1]].erase(find(adjList[path[l-1]].begin(),adjList[path[l-1]].end(),path[l]));
adjList[path[l]].erase(find(adjList[path[l]].begin(),adjList[path[l]].end(),path[l-1]));
adjList[path[l]].pb(v),adjList[v].pb(path[l]);
adjList[path[l-1]].pb(v),adjList[v].pb(path[l-1]);
if (u != v) adjList[u].pb(v),adjList[v].pb(u);
done[v] = 1;
return 0;
}
else if (v == s) {
for (i = 0; i < adjList[s].size(); i++) {
int t = adjList[s][i];
if ((t == parent[s]) || (t == heavy[s])) continue;
if (lca(tail[chain[t]],u) != s) {
if (lca(t,u) != t) {
v = lca(t,u);
adjList[s].erase(find(adjList[s].begin(),adjList[s].end(),t));
adjList[t].erase(find(adjList[t].begin(),adjList[t].end(),s));
adjList[t].pb(v),adjList[v].pb(s);
adjList[s].pb(v),adjList[v].pb(t);
if (u != v) adjList[u].pb(v),adjList[v].pb(u);
done[v] = 1;
return 0;
}
else add(u,t);
return 0;
}
}
adjList[s].pb(u);
adjList[u].pb(s);
return 0;
}
else {
vi path;
int t = s;
while (t != -1) path.pb(t),t = heavy[t];
int l = 1,r = path.size()-1;
while (l < r) {
int m = (l+r) / 2;
if (lca(path[m],u) == v) r = m;
else l = m+1;
}
add(u,path[l]);
return 0;
}
}
void Solve(int N) {
int i;
for (i = 0; i < N; i++) fill(M[i],M[i]+N,-1);
done[0] = 1;
for (i = 1; i < N; i++) {
if (!done[i]) {
doDFS(0,-1),c = 0,doHLD(0,-1),c++;
add(i,0),done[i] = 1;
}
}
doDFS(0,-1);
for (i = 1; i < N; i++) {
if (parent[i] < i) Bridge(parent[i],i);
else Bridge(i,parent[i]);
}
}
