#include "islands.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef long double ld;
typedef pair<ll, ll> pll;
#define FOR(i, a, b) for(int i = a; i < b; i++)
#define ROF(i, a, b) for(int i = a; i >= b; i--)
#define ms memset
#define pb push_back
#define fi first
#define se second
int mat[1000][1000][2];
vi ans; vi p(1000,-1); vi used(1000);
int n;
void dfs(int u){
used[u]=1;
FOR(v,0,n){
if (mat[u][v][0] == -1) continue;
if (p[u]==v) continue;
if (mat[u][v][1] != -1){
cout << "PATH\n";
vi path;
int w = u;
while (w != 0){
path.pb(w); w=p[w];
}
path.pb(0);
ROF(i,path.size()-1,1){
ans.pb(mat[path[i]][path[i-1]][0]);
}
//e0[0], e1[0], e0[1], e0[0], e1[0], e0[1]
vi path2 = {mat[u][v][0], mat[v][u][0], mat[u][v][1]};
FOR(i,0,2){
FOR(j,0,3) ans.pb(path2[j]);
}
FOR(i,1,path.size()){
ans.pb(mat[path[i]][path[i-1]][0]);
}
return;
}
if (used[v]){
// cycle 0-v-u
cout << "CYCLE\n";
vi path;
int w = u;
while (w != 0){
path.pb(w); w=p[w];
}
path.pb(0);
//path 0-v
ROF(i,path.size()-1,1){
ans.pb(mat[path[i]][path[i-1]][0]);
}
vi cyc;
w = u;
while (w != v){
cyc.pb(w); w=p[w];
}
cyc.pb(v);
//cycle 1
ans.pb(mat[v][u][0]);
FOR(i,1,cyc.size()){
ans.pb(mat[cyc[i-1]][cyc[i]][0]);
}
//cycle 2
ROF(i,cyc.size()-1,1){
ans.pb(mat[cyc[i]][cyc[i-1]][0]);
}
ans.pb(mat[u][v][0]);
//reverse cycle 1
ROF(i,cyc.size()-1,1){
ans.pb(mat[cyc[i-1]][cyc[i]][0]);
}
ans.pb(mat[v][u][0]);
//reverse cycle 2
ans.pb(mat[u][v][0]);
FOR(i,1,cyc.size()){
ans.pb(mat[cyc[i]][cyc[i-1]][0]);
}
//path v-0
FOR(i,1,path.size()){
ans.pb(mat[path[i]][path[i-1]][0]);
}
return;
}
p[v] = u; used[v] = 1;
dfs(v);
}
}
variant<bool, vi> find_journey(int N, int M, vi U, vi V) {
n=N;
if (N == 2){
vi e0, e1;
FOR(i,0,M){
if (U[i]==0) e0.pb(i);
else e1.pb(i);
}
if (e0.size() < 2 || e1.size() < 1) return false;
return vi({e0[0], e1[0], e0[1], e0[0], e1[0], e0[1]});
}
/*
if (N <= 400 && M == N*(N-1)){
vii p = {{0,1},{1,2},{2,0},{0,2},{2,1},{1,0}};
vi l(6);
FOR(i,0,M){
FOR(j,0,6){
if (p[j] == ii({U[i],V[i]})){
l[j] = i;
}
}
}
return vi({l[0],l[1],l[2],l[3],l[4],l[5],l[2],l[1],l[0],l[5],l[4],l[3]});
}
*/
if (N <= 1000 && U[0] != U[1]){
ms(mat, -1, sizeof(mat));
FOR(i,0,M){
// labelling edges
int pos = 0;
if (mat[U[i]][V[i]][0] != -1) pos = 1;
mat[U[i]][V[i]][pos] = i;
}
dfs(0);
if (ans.empty()) return false;
return ans;
/*
vi p(N,-1);
vi bfs; bfs.pb(0);
vi used(N); used[0] = 1;
FOR(k,0,bfs.size()){
int u = bfs[k];
FOR(i,0,N){
if (mat[u][i][0] == -1) continue;
if (used[i] && p[u] != i){
// cycle found
vi paru; int v = u;
while (v != 0){
paru.pb(v);
v = p[v];
}
paru.pb(0);
vi pari; v = i;
while (v != 0){
pari.pb(v); v = p[v];
}
pari.pb(0);
reverse(paru.begin(),paru.end());
reverse(pari.begin(),pari.end());
int a = 0;
vi ans;
//path from 0 to cycle
FOR(j,1,min(paru.size(),pari.size())){
if (paru[j] == pari[j]){
ans.pb(mat[paru[j-1]][paru[j]][0]);
a=j;
}else{
break;
}
}
//first loop
FOR(j,a+1,paru.size()){
ans.pb(mat[paru[j-1]][paru[j]][0]);
}
ans.pb(mat[u][i][0]);
ROF(j,pari.size()-1,a+1){
ans.pb(mat[pari[j]][pari[j-1]][0]);
}
//second loop
FOR(j,a+1,pari.size()){
ans.pb(mat[pari[j-1]][pari[j]][0]);
}
ans.pb(mat[i][u][0]);
ROF(j,paru.size()-1,a+1){
ans.pb(mat[paru[j]][paru[j-1]][0]);
}
//reverse 1st loop
FOR(j,a+1,pari.size()){
ans.pb(mat[pari[j]][pari[j-1]][0]);
}
ans.pb(mat[u][i][0]);
ROF(j,paru.size()-1,a+1){
ans.pb(mat[paru[j-1]][paru[j]][0]);
}
//reverse 2nd loop
FOR(j,a+1,paru.size()){
ans.pb(mat[paru[j]][paru[j-1]][0]);
}
ans.pb(mat[i][u][0]);
ROF(j,pari.size()-1,a+1){
ans.pb(mat[pari[j-1]][pari[j]][0]);
}
//path back to 0
ROF(j,a,1){
ans.pb(mat[paru[j]][paru[j-1]][0]);
}
return ans;
}
if (mat[u][i][1] != -1 && p[u] != i){
// double edge found, solution from Subtask 1
vi par; int v = u;
while (v != 0){
par.pb(v);
v = p[v];
}
par.pb(0);
reverse(par.begin(), par.end());
vi ans;
FOR(j,0,par.size()-1){
ans.pb(mat[par[j]][par[j+1]][0]); //path 0 -> u
}
// e0[0], e1[0], e0[1], e0[0], e1[0], e0[1]
vi path = {mat[u][i][0], mat[i][u][0], mat[u][i][1], mat[u][i][0], mat[i][u][0], mat[u][i][1]};
FOR(j,0,6) ans.pb(path[j]);
ROF(j,par.size()-2,0){
ans.pb(mat[par[j]][par[j+1]][0]); //path u -> 0
}
return ans;
}
if (used[i]) continue;
used[i] = 1; p[i] = u;
bfs.pb(i);
}
}
*/
}
return false;
}
