//*** Bismillah ***//
#pragma GCC optimize("O3", "fast-math", "unroll-loops", "no-stack-protector")
#include <bits/stdc++.h>
using namespace std;
#if !defined(ONLINE_JUDGE) and !defined(EVAL)
#include "template/debug.h"
#else
#define d(x...)
#endif
#define fr first
#define er erase
#define sc second
#define in insert
#define ll long long
#define pb push_back
#define vll vector<ll>
#define pll pair<ll,ll>
#define ull unsigned ll
#define vpll vector<pll>
#define len(x) (ll) x.size()
#define all(x) x.begin(),x.end()
const ll INF = 1e9;
const ll INFL = 1e18;
const ll MOD = 1e9+7;
// const ll MOD = 998244353;
const ll maxn = 1e5+5;
ll n,m,k=0;
vll g[maxn];
bool vis[maxn];
ll spec, root, dp[maxn][2][2][2][2];
void dfs(ll u, ll p = -1){
vis[u] = 1;
for(auto v : g[u]){
if(v == p) continue;
if(vis[v]){
root = v;
spec = u;
return;
}
dfs(v, u);
if(root != 0) return;
}
}
#define dpp dp[u][c][up][rt][sp]
ll get(ll u, ll c, ll up, ll rt, ll sp, ll p = -1){
if(u == spec and c != sp) return dpp = INFL;
if(u == root and c != rt) return dpp = INFL;
if(up == 1 and u == root and sp) return dpp = INFL;
if(up == 1 and u == spec and rt) return dpp = INFL;
if(dpp != INFL) return dpp;
ll cm = c;
for(auto v : g[u]){
if(v == p) continue;
cm += get(v, 0, c, rt, sp, u);
}
if(up or (u == root and sp) or (u == spec and rt)){
return cm;
}
else{
ll cv = INFL;
for(auto v : g[u]){
if(v == p) continue;
cv = min(cv,
cm - get(v, 0, c, rt, sp, u) + get(v, 1, c, rt, sp, u));
}
return cv;
}
}
void _(ll &tt){
cin >> n;
for(ll i = 1, a, b; i <= n; i ++){
cin >> a >> b;
g[a].pb(b);
g[b].pb(a);
}
ll leaf = -1;
for(ll i = 1; i <= n; i ++) if(len(g[i]) == 1){ leaf = i; break; }
if(leaf == -1){
cout << (n % 4 == 0 ? n / 2 : -1) << '\n';
return;
}
dfs(1);
g[root].erase(find(all(g[root]), spec));
g[spec].erase(find(all(g[spec]), root));
d(spec, root);
for(ll i = 1; i <= n; i ++){
for(auto j : {0, 1}) for(auto q : {0, 1}) for(auto l : {0, 1}) for(auto p : {0, 1}){
dp[i][j][q][l][p] = INFL; // yea, ik
}
}
ll cv = INFL;
for(auto i : {0, 1}) for(auto j : {0, 1}){
cv = min(cv, get(root, i, 0, i, j));
}
cout << (cv == INFL ? -1 : cv) << '\n';
}
signed main() {
ll tm = clock();
cin.tie(0)->sync_with_stdio(0);
ll t = 1;
// cin >> t;
for(ll tt = 1; tt <= t; tt ++) {
_(tt);
}
cerr << "\n\033[1;31mTime: \033[1;30m" \
<< (double)(clock()-tm)/1000000 << "\033[1;32m seconds\n";
}
