#include <cstdio>
#include <iostream>
#include <cassert>
#include <vector>
#include <cstdlib>
#include <string>
#include <utility>
#include <tuple>
using namespace std;
std::vector<int> find_roads(int n, std::vector<int> u, std::vector<int> v);
int count_common_roads(const std::vector<int>& r);
bool isSubtask1(int n) {return n<=7;}
bool isSubtask2(int n) {return n<=50;}
bool isSubtask3(int n) {return n<=240;}
void dfs3(int startNode, int startEdge, int parent, int now, vector<vector<pair<int,int>>>& edgeL,
vector<int>& r2, vector<int>& dNode, vector<vector<int>>& alterEdge) {
dNode[now]=1;
for(auto& elem: edgeL[now]) {
int nextNode,nextEdge; tie(nextNode,nextEdge) = elem;
if (nextNode==parent) continue;
if (nextNode==startNode) {alterEdge[startEdge].push_back(nextEdge); continue;}
if (!dNode[nextNode]) {
r2.push_back(nextEdge);
dfs3(startNode,startEdge,now,nextNode,edgeL,r2,dNode,alterEdge);
}
}
return;
}
vector<int> subtask3(int n, std::vector<int>& u, std::vector<int>& v) {
int m = u.size();
vector<int> r;
vector<int> treeEdge(m);
vector<bool> testedEdge(m);
// Edge list
vector<vector<pair<int,int>>> edgeL(n);
for(int i=0; i<m; i++) {
edgeL[u[i]].push_back(make_pair(v[i],i));
edgeL[v[i]].push_back(make_pair(u[i],i));
}
// printf("Edge list\n");
// for(int i=0; i<n; i++) {printf("%d: ",i); for(auto& elem: edgeL[i]) printf("(%d,%d) ",elem.first,elem.second); printf("\n");} printf("\n");
for(int startNode=0; startNode<n; startNode++) {
// printf("------ startNode = %d ------\n",startNode);
vector<int> dNode(n); vector<vector<int>> alterEdge(m);
dNode[startNode] = 1;
vector<int> r2, r2StartEdgeIdx;
int secondNode,startEdge;
for(auto& elem: edgeL[startNode]) {
tie(secondNode,startEdge) = elem;
if (dNode[secondNode]) continue;
r2.push_back(startEdge);
r2StartEdgeIdx.push_back(r2.size()-1);
dfs3(startNode,startEdge,startNode,secondNode,edgeL,r2,dNode,alterEdge);
}
// printf("r2: "); for(int elem: r2) printf("%d ",elem); printf("\n");
// printf("r2StartEdgeIdx: "); for(int elem: r2StartEdgeIdx) printf("%d ",elem); printf("\n");
// printf("alterEdge: \n");
// for(int i=0; i<n; i++) { printf("%d: ",i); for(auto& elem: alterEdge[i]) printf("%d ",elem); printf("\n");}
// int defaultCount = count_common_roads(r2);
// tested가 있는 경우에 그것을 가지고 untested의 treeEdge 여부 계산가능
for(int startEdgeIdx: r2StartEdgeIdx) {
vector<int> result;
int maxValue = -1;
int startEdge = r2[startEdgeIdx], newStartEdge = r2[startEdgeIdx];
vector<int> cycle; cycle.push_back(startEdge);
for(int anEdge: alterEdge[startEdge]) cycle.push_back(anEdge);
// printf("cycle: "); for(int elem: cycle) printf("%d ",elem); printf("\n");
bool hasTestedEdge = false;
for(int anEdge: cycle)
if (testedEdge[anEdge]) {hasTestedEdge = true; newStartEdge = anEdge; break;}
// printf("hasTestedEdge = %d, newStartEdge = %d\n",hasTestedEdge,newStartEdge);
if (hasTestedEdge) {
r2[startEdgeIdx] = newStartEdge;
maxValue = count_common_roads(r2);
if (!treeEdge[newStartEdge]) maxValue++;
r2[startEdgeIdx] = startEdge;
}
// printf("maxValue = %d\n",maxValue);
for(int anEdge: cycle) {
int temp;
if (testedEdge[anEdge]) {
temp = treeEdge[anEdge]? maxValue:maxValue-1;
}
else {
r2[startEdgeIdx] = anEdge;
testedEdge[anEdge] = true;
temp = count_common_roads(r2);
maxValue = max(maxValue,temp);
}
result.push_back(temp);
}
// printf("result: "); for(int elem: result) printf("%d ",elem); printf("\n");
for(int j=0; j<result.size(); j++)
if (result[j] == maxValue) treeEdge[cycle[j]] = 1;
r2[startEdgeIdx] = startEdge;
// printf("testedEdge: "); for(bool elem: testedEdge) printf("%d ",elem); printf("\n");
// printf("treeEdge: "); for(int elem: treeEdge) printf("%d ",elem); printf("\n\n");
}
}
for(int i=0; i<m; i++) if (treeEdge[i]) r.push_back(i);
// printf("r: "); for(int elem: r) printf("%d ",elem); printf("\n");
return r;
}
void dfs(int parent, int now, std::vector<int>& visit, std::vector<vector<int>>& edgeL) {
visit[now]=1;
for(int elem: edgeL[now])
if (elem!=parent && !visit[elem])
dfs(now,elem,visit,edgeL);
return;
}
bool isTree(std::vector<int>& r, std::vector<int>& u, std::vector<int>& v) {
int n = r.size()+1;
std::vector<vector<int>> edgeL(n);
for(int i=0; i<n-1; i++) {
int s = u[r[i]], e = v[r[i]];
edgeL[s].push_back(e);
edgeL[e].push_back(s);
}
vector<int> visit(n,0);
dfs(-1,u[r[0]],visit,edgeL);
for(int i=0; i<n; i++)
if(!visit[i]) return false;
return true;
}
bool selectEdges(int cnt, int start, std::vector<int>& r, std::vector<int>& u, std::vector<int>& v){
int n = r.size()+1, m = u.size();
if (cnt == n-1){
if(isTree(r,u,v) && count_common_roads(r)== n-1) return true;
else return false;
}
for(int i=start; i<m; i++){
r[cnt] = i;
if (selectEdges(cnt+1,i+1,r,u,v)) return true;
}
return false;
}
std::vector<int> subtask1(int n, std::vector<int>& u, std::vector<int>& v) {
std::vector<int> r(n-1), zero(n-1,-1);
if (selectEdges(0,0,r,u,v)) return r;
else return zero;
}
std::vector<int> find_roads(int n, std::vector<int> u, std::vector<int> v) {
return subtask3(n,u,v);
// if (isSubtask1(n))
return subtask1(n,u,v);
}
