#include "bits/stdc++.h"
#define st first
#define nd second
using lint = int64_t;
constexpr int MOD = int(1e9) + 7;
constexpr int INF = 0x3f3f3f3f;
constexpr int NINF = 0xcfcfcfcf;
constexpr lint LINF = 0x3f3f3f3f3f3f3f3f;
const long double PI = acosl(-1.0);
// Returns -1 if a < b, 0 if a = b and 1 if a > b.
int cmp_double(double a, double b = 0, double eps = 1e-9) {
return a + eps > b ? b + eps > a ? 0 : 1 : -1;
}
using namespace std;
int n;
array<array<lint,2>, 2> clear;
vector<array<array<lint,2>, 2>> dp;
vector<vector<int>> g;
int root = -1, rootColor = -1;
int pairOfRoot = -1, pairOfRootColor = -1;
const int RED = 0, BLUE = 1;
int solve(int u, int color, int parColor, int p){
auto &DP = dp[u][color][parColor];
if(DP != -1) return DP;
DP = INF;
if (u == root && color != rootColor) return DP;
if (u == pairOfRoot && color != pairOfRootColor) return DP;
if (u == pairOfRoot && parColor == BLUE && rootColor == BLUE) return DP;
lint sumRed = color;
for(auto v:g[u])
if(v != p)
sumRed += solve(v, RED, color, u);
if (parColor == BLUE) return DP = min(DP, sumRed);
if (u == root && pairOfRootColor == BLUE) return DP = min(DP, sumRed);
if (u == pairOfRoot && rootColor == BLUE) return DP = min(DP, sumRed);
for(auto v:g[u])
if(v != p)
DP = min(DP, sumRed - solve(v, RED, color, u) + solve(v, BLUE, color, u) );
return DP;
}
vector<bool> visited;
void findRoot(int u, int p){
visited[u] = true;
for(int w: g[u])
if(w != p){
if(visited[w]){
root = u;
pairOfRoot = w;
} else
findRoot(w, u);
}
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
cin>>n;
g.resize(n+1);
vector<int> degree(n+1);
for (int i=0; i<n; i++) {
int a, b;
cin>>a>>b;
g[a].push_back(b);
g[b].push_back(a);
degree[a]++;
degree[b]++;
}
bool bigCycle = true;
for (int u=1; u<=n; u++) {
if(degree[u] != 2)
bigCycle = false;
}
if(bigCycle){
if(n % 4 == 0) cout<<n/2;
else cout<<"-1";
return 0;
}
visited.resize(n+1);
findRoot(1, -1);
//cout<<root<<" "<<pairOfRoot<<"\n";
g[root].erase(find(g[root].begin(), g[root].end(), pairOfRoot));
g[pairOfRoot].erase(find(g[pairOfRoot].begin(), g[pairOfRoot].end(), root));
for(int i=0; i<2; i++)
for(int j=0; j<2; j++)
clear[i][j] = -1;
int ans = INF;
{
dp.assign(n+1, clear);
rootColor = RED;
pairOfRootColor = RED;
ans = min(ans, solve(root, rootColor, 0, pairOfRoot));
}
{
dp.assign(n+1, clear);
rootColor = RED;
pairOfRootColor = BLUE;
ans = min(ans, solve(root, rootColor, 0, pairOfRoot));
}
{
dp.assign(n+1, clear);
rootColor = BLUE;
pairOfRootColor = RED;
ans = min(ans, solve(root, rootColor, 0, pairOfRoot));
}
{
dp.assign(n+1, clear);
rootColor = BLUE;
pairOfRootColor = BLUE;
ans = min(ans, solve(root, rootColor, 0, pairOfRoot));
}
if(ans == INF) ans = -1;
cout<<ans<<"\n";
return 0;
}
/*
[ ]Leu o problema certo???
[ ]Ver se precisa de long long
[ ]Viu o limite dos fors (é n? é m?)
[ ]Tamanho do vetor, será que é 2e5 em vez de 1e5??
[ ]Testar sample
[ ]Testar casos de borda
[ ]1LL no 1LL << i
[ ]Testar mod (é 1e9+7, mesmo?, será que o mod não ficou negativo?)
*/
