This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
# include <bits/stdc++.h>
# define pb push_back
# define ff first
# define ss second
# define nl "\n"
# define sz(x) ((int)(x).size())
# define deb(x) cerr << #x << " = " << x << endl;
# define pll pair <ll, ll>
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const ll maxn = 1e6 + 25;
const ll inf = 1e18 + 0;
const ll mod = 1e9 + 123;
const ll dx[] = {-1, 1, 0, 0};
const ll dy[] = {0, 0, -1, 1};
using namespace std;
ll n, col[maxn];
vector <ll> g[maxn];
bool used[maxn];
bool bad;
void ok (ll v)
{
used[v] = 1;
ll cnt = 0;
for (ll to : g[v])
{
cnt += (col[to] == 1);
}
if (cnt != 1)
{
bad = 1;
}
for (ll to : g[v])
{
if (!used[to])
{
ok(to);
}
}
}
void ma1n (/* SABR */)
{
cin >> n;
for (ll i = 1, u, v; i <= n; ++i)
{
cin >> u >> v;
g[u].pb(v);
g[v].pb(u);
}
if (n <= 20)
{
ll ans = n + 1;
for (ll mask = 0; mask < (1LL << n); ++mask)
{
bad = 0;
ll cnt = 0;
for (ll i = 0; i < n; ++i)
{
used[i + 1] = 0;
col[i + 1] = 0;
if (mask & (1LL << i))
{
cnt++;
col[i + 1] = 1;
}
}
ok(1);
if (!bad)
{
ans = min(ans, cnt);
}
}
if (ans == n + 1) ans = -1;
cout << ans;
}
else
{
bool sub1 = 1;
for (ll i = 1; i <= n; ++i)
{
sub1 &= (sz(g[i]) == 2);
}
if (sub1)
{
if (n % 4 == 0)
{
cout << n / 2 << nl;
}
else
{
cout << -1 << nl;
}
}
}
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
// freopen("spainting.in", "r", stdin);
// freopen("spainting.out", "w", stdout);
int ttt = 1;
// cin >> ttt;
for (int test = 1; test <= ttt; ++test)
{
// cout << "Case " << test << ":" << ' ';
ma1n();
}
return 0;
}
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