#include<bits/stdc++.h>
using namespace std;
#define foru(i,a,b) for(int i=(a); i<=(b); ++i)
#define ford(i,a,b) for(int i=(a); i>=(b); --i)
#define rep(i,a) for(int i=0; i<(a); ++i)
#define sz(a) (int)(a).size()
#define all(a) (a).begin(),(a).end()
#define bit(s,i) (((s)>>(i))&1)
#define ii pair<int,int>
#define vi vector<int>
#define vii vector<ii>
#define fi first
#define se second
#define ll long long
#define eb emplace_back
#define pb push_back
#define __builtin_popcount __builtin_popcountll
#define _ << " " <<
template <class X, class Y> bool maxi(X &x, Y y){return x<y?x=y,true:false;}
template <class X, class Y> bool mini(X &x, Y y){return x>y?x=y,true:false;}
const int N=1e5+5;
const int INF=1e9;
int n;
vi adj[N];
void input(){
cin>>n;
foru(i,1,n){
int u,v; cin>>u>>v;
adj[u].eb(v); adj[v].eb(u);
}
}
int trace[N],vis[N]; bool inCycle[N];
vi cycle;
void dfs1(int u, int p=-1){
vis[u]=1;
for(int v:adj[u]) if(v!=p){
if(sz(cycle)) return;
if(vis[v]){
int t=u;
while(t!=v){
cycle.eb(t); t=trace[t];
}
cycle.eb(v);
} else{
trace[v]=u;
dfs1(v,u);
}
}
}
void findCycle(){
dfs1(1);
for(int i:cycle) inCycle[i]=1;
}
int dp1[N][2][2]; /// blue-eye?, is-seen?
int f[2][2];
void dfs2(int u, int p=-1){
dp1[u][0][0]=0; dp1[u][1][0]=1;
for(int v:adj[u]) if(v!=p && !inCycle[v]){
dfs2(v,u);
f[0][1]=min(dp1[u][0][0]+dp1[v][1][1], dp1[u][0][1]+dp1[v][0][1]);
f[0][0]=dp1[u][0][0]+dp1[v][0][1];
f[1][1]=min(dp1[u][1][0]+dp1[v][1][0], dp1[u][1][1]+dp1[v][0][0]);
f[1][0]=dp1[u][1][0]+dp1[v][0][0];
rep(i,2) rep(j,2) dp1[u][i][j]=f[i][j];
}
}
void dpTree(){
memset(dp1,0x3f,sizeof(dp1));
for(int i:cycle) dfs2(i);
}
int dp2[N][2][2][2][2];///status of 0, status of cycle[i]
void dpCycle(){
memset(dp2,0x3f,sizeof(dp2));
rep(i,2) rep(j,2) dp2[cycle[0]][i][j][i][j]=dp1[cycle[0]][i][j];
rep(i,sz(cycle)-1) rep(h1,2) rep(h2,2) rep(j,2) rep(k,2){
/// ta co trang thai cua i
/// chuyen sang trang thai cua i+1 nhu the nao ???
/// dau tien for trang thai cua i+1
/// neu trang thai i+1 dam trang thai cua i -> fail
/// neu ko -> cong vao
rep(nj,2) rep(nk,2){
if(k && nj) continue;
if(j && nk) continue;
if(i!=0 && !k && !nj) continue;
if(i==0 && h2 && nj) continue;
if(i==0){
mini(dp2[cycle[i+1]][h1][h2|nj][nj][nk|j],dp2[cycle[i]][h1][h2][j][k]+dp1[cycle[i+1]][nj][nk]);
} else{
mini(dp2[cycle[i+1]][h1][h2][nj][nk|j],dp2[cycle[i]][h1][h2][j][k]+dp1[cycle[i+1]][nj][nk]);
}
}
}
int res=INF;
rep(j1,2) rep(k1,2) rep(j2,2) rep(k2,2){
if(k1 && j2) continue;
if(k2 && j1) continue;
if(!k2 && !j1) continue;
if(!k1 && !j2) continue;
mini(res, dp2[cycle.back()][j1][k1][j2][k2]);
}
cout<<(res==INF?-1:res)<<'\n';
}
void solve(){
input();
findCycle();
dpTree();
dpCycle();
}
int32_t main(){
#define task "test"
if(fopen(task".inp", "r")){
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
cin.tie(0)->sync_with_stdio(0);
int tc=1; //cin>>tc;
foru(i,1,tc){
solve();
}
}
