This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast,O2,O3,unroll-loops")
#pragma GCC target("avx2")
#include <bits/stdc++.h>
#include <random>
using namespace std;
void debug_out() { cerr << endl; }
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << "[" << H << "]";
debug_out(T...);
}
#ifdef dddxxz
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
#define SZ(s) ((int)s.size())
#define all(x) (x).begin(), (x).end()
#define lla(x) (x).rbegin(), (x).rend()
#define bpc(x) __builtin_popcount(x)
#define bpcll(x) __builtin_popcountll(x)
clock_t startTime;
double getCurrentTime() {
return (double) (clock() - startTime) / CLOCKS_PER_SEC;
}
#define MP make_pair
typedef long long ll;
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
const double eps = 0.000001;
const int MOD = 1e9 + 7;
const int INF = 1000000101;
const long long LLINF = 1223372000000000555;
const int N = 1e6 + 3e2;
const int M = 1111;
vector<int> g[N];
set<int> groups[N];
int color[N];
void solve(int TC) {
int n;
cin >> n;
fill(color + 1, color + n + 1, -1);
for (int i = 1; i <= n; i++){
int x, y;
cin >> x >> y;
g[x].push_back(y);
g[y].push_back(x);
}
for (int i = 1; i <= n; i++){
for (int j : g[i]) groups[i].insert(j);
}
bool ok = false;
for (int i = 1; i <= n; i++){
if (g[i].size() == 1){
color[g[i][0]] = 1;
ok = true;
}
}
if (!ok){
cout << (n % 4 == 0 ? n / 2 : -1);
return;
}
for (int it = 1; it <= (n + 5) * (n + 5); it++){
for (int i = 1; i <= n; i++){
int black = 0, white = 0;
for (int j : groups[i]){
if (color[j] == 0) white++;
if (color[j] == 1) black++;
}
int sz = (int)groups[i].size();
if (black == 1){
for (int j : groups[i]){
if (color[j] == -1) color[j] = 0;
}
} else if (white == sz - 1){
for (int j : groups[i]){
if (color[j] == -1) color[j] = 1;
}
}
}
}
// for (int i = 1; i <= n; i++) cout << color[i] << ' '; cout << endl;
int ans = 0;
for (int i = 1; i <= n; i++){
assert(color[i] != -1);
ans += color[i];
int cnt = 0;
for (int j : g[i]) cnt += color[j] == 1;
if (cnt != 1){
cout << -1;
return;
}
}
cout << ans << endl;
}
int main() {
startTime = clock();
ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
#ifdef dddxxz
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
int TC = 1;
// cin >> TC;
for (int test = 1; test <= TC; test++) {
//debug(test);
//cout << "Case #" << test << ": ";
solve(test);
}
#ifdef dddxxz
cerr << endl << "Time: " << int(getCurrentTime() * 1000) << " ms" << endl;
#endif
return 0;
}
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