#include <bits/stdc++.h>
#define ll long long
#define pii pair<int,int>
#define pll pair<ll,ll>
#define rep(i,m,n) for(int i=(m); i<=(n); i++)
#define reb(i,m,n) for(int i=(m); i>=(n); i--)
#define iter(id, v) for(auto id : v)
#define fs first
#define se second
#define MP make_pair
#define pb push_back
#define bit(msk, i) ((msk >> i) & 1)
#define SZ(v) (ll)v.size()
#define ALL(v) v.begin(),v.end()
using namespace std;
mt19937_64 rd(chrono :: steady_clock :: now ().time_since_epoch().count());
ll Rand (ll l, ll r) { return uniform_int_distribution<ll> (l, r) (rd); }
const int N = 1e5 + 7;
const int Mod = 1e9 + 7; ///loonf mod sai
const int INF = 1e9;
const ll BASE = 137;
const int szBL = 320;
int n, m;
int a[N];
vector<int> ke[N];
int dp[N][2][2], f[N][2][2], Val[N][2][2];
vector<int> C;
int dd[N];
void Find_cycle () {
C = {-1};
int ok = 0;
function<void(int, int)> dfs = [&] (int u, int p) {
dd[u] = 1;
C.pb(u);
iter (&v, ke[u])
if (v != p && !ok) {
if (dd[v] == 1) {
auto R = find(C.begin() + 1, C.end(), v);
if (R != C.begin()) {
C.erase(C.begin() + 1, R);
}
ok = 1;
return;
}
dfs(v, u);
}
if (!ok) C.pop_back();
};
dfs(1, 0);
m = SZ(C) - 1;
rep (i, 1, n) dd[i] = 0;
rep (i, 1, m) dd[C[i]] = 1;
}
void Assign (int u, vector<int> &child) {
if (SZ(child) == 0) {
f[u][1][0] = 1;
f[u][0][0] = 0;
return;
}
f[u][0][0] = 0;
f[u][1][0] = 1;
vector<int> vec00, vec10;
iter (&v, child) {
if (f[v][0][1] > n && SZ(vec00) < 2) vec00.pb(v);
if (f[v][0][0] > n && SZ(vec10) < 2) vec10.pb(v);
f[u][0][0] = min (INF, f[u][0][0] + f[v][0][1]);
f[u][1][0] = min (INF, f[u][1][0] + f[v][0][0]);
}
auto calc = [&] (int t, int p, vector<int> &vec) {
int nt, np, pt, pp;
if (t == 0 && p == 1) pt = 0, pp = 1, nt = 1, np = 1;
else pt = 0, pp = 0, nt = 1, np = 0;
if (SZ(vec) == 1) {
int alterV = vec[0];
f[u][t][p] = t;
iter (&v, child) {
if (v != alterV) f[u][t][p] = min (INF, f[u][t][p] + f[v][pt][pp]);
else f[u][t][p] = min (INF, f[u][t][p] + f[v][nt][np]);
}
}
else if (SZ(vec) == 0) {
int Min = INF;
f[u][t][p] = t;
iter (&v, child) {
f[u][t][p] = min (INF, f[u][t][p] + f[v][pt][pp]);
Min = min(Min, -f[v][pt][pp] + f[v][nt][np]);
}
f[u][t][p] = min(INF, f[u][t][p] + Min);
}
else f[u][t][p] = INF;
};
calc(0, 1, vec00);
calc(1, 1, vec10);
}
void dfs (int u, int p) {
vector<int> child;
iter (&v, ke[u]) {
if (!dd[v] && v != p) {
dfs(v, u);
child.pb(v);
}
}
Assign(u, child);
}
int calc (int t, int p) {///con 1 trang thai nao va look con nao ben phai chua
rep (i, 1, m)
rep (j, 0, 1)
rep (t, 0, 1) dp[i][j][t] = INF;
if (t == 1 && p == 1) {
dp[2][0][1] = min(INF, Val[1][1][1] + Val[2][0][0]);
dp[2][1][1] = min(INF, Val[1][1][0] + Val[2][1][0]);
}
else if (t == 1 && p == 0) {
dp[2][0][1] = min(INF, Val[1][1][0] + Val[2][0][0]);
}
else if (t == 0 && p == 1) {
rep (i, 0, 1) {
dp[2][0][i] = min(INF, Val[1][0][1] + Val[2][0][i]);
dp[2][1][i] = min(INF, Val[1][0][0] + Val[2][1][i]);
}
}
else {
rep (i, 0, 1) dp[2][0][i] = min(INF, Val[1][0][0] + Val[2][0][i]);
}
rep (i, 3, m) {
dp[i][0][0] = min({INF,
dp[i - 1][0][1] + Val[i][0][0]});
dp[i][0][1] = min({INF,
dp[i - 1][0][1] + Val[i][0][1],
dp[i - 1][1][1] + Val[i][0][0]});
dp[i][1][0] = min({INF,
dp[i - 1][0][0] + Val[i][1][0]});
dp[i][1][1] = min({INF,
dp[i - 1][1][0] + Val[i][1][0],
dp[i - 1][0][0] + Val[i][1][1]});
}
if (t == 1 && p == 1)
return dp[m][0][0];
else if (t == 1 && p == 0)
return dp[m][1][0];
else if (t == 0 && p == 1)
return dp[m][0][1];
else
return dp[m][1][1];
}
void solution() {
cin >> n;
rep (i, 1, n) {
int u, v;
cin >> u >> v;
ke[u].pb(v);
ke[v].pb(u);
}
Find_cycle();
rep (i, 1, n)
rep (j, 0, 1)
rep (t, 0, 1)
f[i][j][t] = INF;
rep (i, 1, m) {
int u = C[i];
dfs(u, 0);
}
rep (i, 1, m)
rep (j, 0, 1)
rep (t, 0, 1) {
Val[i][j][t] = f[C[i]][j][t];
}
int res = INF;
rep (i, 0, 1)
rep (j, 0, 1) {
res = min(res, calc(i, j));
}
if (res > n)
cout << -1 <<"\n";
else
cout << res <<"\n";
}
#define file(name) freopen(name".inp","r",stdin); \
freopen(name".out","w",stdout);
int main () {
// file("c");
ios_base :: sync_with_stdio(false); cin.tie(0); cout.tie(0);
int num_Test = 1;
// cin >> num_Test;
while (num_Test--)
solution();
}
/*
no bug +9
*/
