This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <algorithm>
#include <string>
#include <sstream>
#include <fstream>
#include <cmath>
#include <queue>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <bits/stdc++.h>
#define lcm(a,b) (a/__gcd(a,b))*b
#define jumanji ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define pb push_back
#define F first
#define S second
#define int long long
#define vi vector<int>
#define ll long long
using namespace std;
const int tam=1e5+5;
vector<vi>G;
int A;
int B;
bool vis[tam];
//find two nodes inside a cycle
void dfs(int u,int p){
vis[u]=1;
for(auto v:G[u]){
if(v==p)continue;
if(vis[v]){
A=u;
B=v;
return;
}
dfs(v,u);
}
}
//dp on tree
int dp[tam][2][2][2][2];
int f(int nodo,int color, int cP,int cA, int cB, int p=0){
int &ans=dp[nodo][color][cP][cA][cB];
if(ans!=-1)return ans;
if(nodo==A && color!=cA)return ans=1e6;
if(nodo==B && color!=cB)return ans=1e6;
if(nodo==B && cA && cP)return ans=1e6;
ans=1e6;
bool ok=true;
if(nodo==A && cB)ok=false;
if(nodo==B && cA)ok=false;
if(cP)ok=false;
//todos tienen que ser cero
int sum=color;
for(auto v:G[nodo]){
if(v==p)continue;
sum+=f(v,0,color,cA,cB,nodo);
}
if(ok==false){
ans=sum;
}else{
//solo tengo que pintar uno
for(auto v:G[nodo]){
if(v==p)continue;
ans=min(ans,sum-f(v,0,color,cA,cB,nodo)+f(v,1,color,cA,cB,nodo));
}
}
return ans;
}
signed main(){
jumanji
memset(dp,-1,sizeof dp);
int n,a,b;
cin>>n;
G.assign(n+1,vi());
vector<pair<int,int>>edges;
for(int i=0;i<=n;i++){
cin>>a>>b;
G[a].pb(b);
G[b].pb(a);
edges.pb({a,b});
}
dfs(1,0);
G.assign(n+1,vi());
for(auto e:edges){
if(e.F==A and e.S==B)continue;
if(e.F==B and e.S==A)continue;
// cout<<e.F<<" f "<<e.S<<endl;
G[e.F].pb(e.S);
G[e.S].pb(e.F);
}
//ambos 1s
int res=1e6;
for(int i=0;i<2;i++){
for(int j=0;j<2;j++){
int curr=f(A,i,0,i,j);
res=min(res,curr);
}
}
// cout<<A<<" "<<B<<endl;
if(res>=1e6){
cout <<-1<<endl;
}else{
cout<<res<<endl;
}
return 0;
}
//Guess i wont be comming to church on sunday
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