#define MOD_TYPE 1 #pragma region Macros #include using namespace std; #if 0 #include #include using Int = boost::multiprecision::cpp_int; using lld = boost::multiprecision::cpp_dec_float_100; #endif #if 1 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #endif using ll = long long int; using ld = long double; using pii = pair; using pll = pair; using pld = pair; template using smaller_queue = priority_queue, greater>; constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353); constexpr int INF = (int)1e9 + 10; constexpr ll LINF = (ll)4e18; constexpr double PI = acos(-1.0); constexpr double EPS = 1e-7; constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0}; constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0}; #define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i) #define rep(i, n) REP(i, 0, n) #define REPI(i, m, n) for (int i = m; i < (int)(n); ++i) #define repi(i, n) REPI(i, 0, n) #define MP make_pair #define MT make_tuple #define YES(n) cout << ((n) ? "YES" : "NO") << "\n" #define Yes(n) cout << ((n) ? "Yes" : "No") << "\n" #define possible(n) cout << ((n) ? "possible" : "impossible") << "\n" #define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n" #define all(v) v.begin(), v.end() #define NP(v) next_permutation(all(v)) #define dbg(x) cerr << #x << ":" << x << "\n"; struct io_init { io_init() { cin.tie(0); ios::sync_with_stdio(false); cout << setprecision(30) << setiosflags(ios::fixed); }; } io_init; template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; } template inline void Fill(A (&array)[N], const T &val) { fill((T *)array, (T *)(array + N), val); } template constexpr istream &operator>>(istream &is, pair &p) noexcept { is >> p.first >> p.second; return is; } template constexpr ostream &operator<<(ostream &os, pair &p) noexcept { os << p.first << " " << p.second; return os; } #pragma endregion template struct Tree { int V; using P = pair; vector> E; vector par; vector depth; vector sub; vector dist; vector> par_double; Tree(int V_) : V(V_) { E.resize(V); depth.resize(V); dist.resize(V); sub.resize(V); } void add_E(int a, int b, T w = T(1), bool direction = false) { E[a].push_back(make_pair(b, w)); if (!direction) E[b].push_back(make_pair(a, w)); } int dfs(int p, int d, T w) { sub[p] = 1; for (auto pi : E[p]) { int v = pi.first; if (par[p] == v) continue; par[v] = p; depth[v] = d + 1; dist[v] = w + pi.second; sub[p] += dfs(v, depth[v], dist[v]); } return sub[p]; } void make_tree(int root = 0) { calculated = false; par.assign(V, -1); par_double.assign(V, vector(25)); depth[root] = 0; dist[root] = T(0); dfs(root, 0, 0); } bool calculated; void calc_double() { for (int i = 0; i < V; i++) par_double[i][0] = par[i]; for (int k = 0; k < 24; k++) { for (int i = 0; i < V; i++) { if (par_double[i][k] == -1) par_double[i][k + 1] = -1; else par_double[i][k + 1] = par_double[par_double[i][k]][k]; } } } int getLCA(int a, int b) { if (!calculated) { calc_double(); calculated = true; } if (a == b) return a; if (depth[a] < depth[b]) swap(a, b); for (int k = 24; k >= 0; k--) { if (par_double[a][k] != -1 && depth[par_double[a][k]] >= depth[b]) a = par_double[a][k]; } if (a == b) return a; for (int k = 24; k >= 0; k--) { if (par_double[a][k] != -1 && par_double[a][k] != par_double[b][k]) { a = par_double[a][k]; b = par_double[b][k]; } } return par_double[a][0]; } int length(int a, int b) { return depth[a] + depth[b] - 2 * depth[getLCA(a, b)]; } int distance(int a, int b) { return dist[a] + dist[b] - 2 * dist[getLCA(a, b)]; } T diameter(int &a, int &b) { T Max(-1); for (int i = 0; i < V; i++) { if (Max < distance(0, i)) Max = distance(0, i), a = i; } for (int i = 0; i < V; i++) { if (Max < distance(a, i)) Max = distance(a, i), b = i; } return Max; } T diameter() { int a, b; return diameter(a, b); } int diameter_l(int &a, int &b) { int Max = -1; for (int i = 0; i < V; i++) { if (Max < length(0, i)) Max = length(0, i), a = i; } for (int i = 0; i < V; i++) { if (Max < length(a, i)) Max = length(a, i), b = i; } return Max; } int diameter_l() { int a, b; return diameter_l(a, b); } }; void solve() { int n; cin >> n; Tree tr(n); vector cnt(n, 0); rep(i, n - 1) { int a, b; cin >> a >> b, a--, b--; cnt[a]++, cnt[b]++; tr.add_E(a, b); } vector leaves; rep(i, n) { if (cnt[i] == 1) { leaves.push_back(i); } } if (leaves.size() == 2) { Yes(1); return; } tr.make_tree(leaves[0]); int d = tr.depth[leaves[1]]; if (d % 2 == 1) { Yes(0); return; } int v = leaves[1]; rep(i, d / 2) v = tr.par[v]; for (auto l : leaves) { if (tr.distance(l, v) != d / 2) { Yes(0); return; } } Yes(cnt[v] == n - 1); } int main() { solve(); }