#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include constexpr long long INF = 1LL << 60; double PI = acos(-1.0); #define rep(i, n) for (ll i = 0; i < (n); ++i) #define rep1(i, n) for (ll i = 1; i <= (n); ++i) #define rrep(i, n) for (ll i = (n - 1); i >= 0; --i) #define perm(c) sort(ALL(c));for(bool c##p=1;c##p;c##p=next_permutation(ALL(c))) #define ALL(obj) (obj).begin(), (obj).end() #define RALL(obj) (obj).rbegin(), (obj).rend() #define pb push_back #define to_s to_string #define len(v) (ll)v.size() #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define print(x) cout << (x) << '\n' #define drop(x) cout << (x) << '\n', exit(0) #define debug(x) cout << #x << ": " << (x) << '\n' using namespace std; typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef pair P; typedef tuple tpl; typedef vector vec; typedef vector> vec2; typedef vector>> vec3; template inline bool chmax(S &a, const T &b) { if (a inline bool chmin(S &a, const T &b) { if (b ostream &operator << (ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator >> (istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T1, typename T2, typename T3 > ostream &operator << (ostream &os, const tuple< T1, T2, T3 > &t) { os << get<0>(t) << " " << get<1>(t) << " " << get<2>(t); return os; } template< typename T1, typename T2, typename T3 > istream &operator >> (istream &is, tuple< T1, T2, T3 > &t) { is >> get<0>(t) >> get<1>(t) >> get<2>(t); return is; } template< typename T > ostream &operator << (ostream &os, const vector< T > &v){ for (int i = 0; i < (int)v.size(); ++i) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator >> (istream &is, vector< T > &v){ for(T &in : v) is >> in; return is; } template< typename T > ostream &operator << (ostream &os, const set< T > &st){ int ct = 0; for(auto& s : st) cout << s << (++ct != st.size() ? " " : ""); return os; } template constexpr set &operator|= (set &st1, const set &st2) { for(auto& s : st2) st1.insert(s); return st1; } template constexpr set &operator-= (set &st1, const set &st2) { for(auto& s : st2) if(st1.count(s)) st1.erase(s); return st1; } template constexpr set &operator&= (set &st1, const set &st2) { auto itr = st1.begin(); while(itr != st1.end()){ if(!st2.count(*itr)) itr = st1.erase(itr); else ++itr; } return st1; } template constexpr set operator| (const set &st1, const set &st2) { set res = st1; res |= st2; return res; } template constexpr set operator- (const set &st1, const set &st2) { set res = st1; res -= st2; return res; } template constexpr set operator& (const set &st1, const set &st2) { set res = st1; res &= st2; return res; } /*--------------------------------- Tools ------------------------------------------*/ template< typename T > vector cumsum(const vector &X){ vector res(X.size() + 1, 0); for(int i = 0; i < X.size(); ++i) res[i + 1] += res[i] + X[i]; return res; } template< typename S, typename T, typename F> pair bisearch(S left, T right, F f) { while(abs(right - left) > 1){ T mid = (right + left) / 2; if(f(mid)) right = mid; else left = mid; } return {left, right}; } template< typename S, typename T, typename F> double trisearch(S left, T right, F f, int maxLoop = 90){ double low = left, high = right; while(maxLoop--){ double mid_left = high / 3 + low * 2 / 3; double mid_right = high * 2 / 3 + low / 3; if(f(mid_left) >= f(mid_right)) low = mid_left; else high = mid_right; } return (low + high) * 0.5; } template< typename F > ll findMinimum(ll L, ll R, F f) { //[L, R) ll lo = L - 1, hi = R - 1; while (lo + 1 != hi) { ll mi = (lo + hi) / 2; if (f(mi) <= f(mi + 1)) hi = mi; else lo = mi; } return hi; } /*--------------------------------- Graph ------------------------------------------*/ struct Graph { struct Edge { ll from, to, weight; Edge() : from(0), to(0), weight(0) {} Edge(ll f, ll t, ll w) : from(f), to(t), weight(w) {} }; using Edges = vector; vector G; Graph() : G() {}; Graph(int N) : G(N) {} Edges operator[](int k) const{ return G[k]; } ll size() const{ return G.size(); } void resize(int N){ G.resize(N); } void add_edge(int a, int b, ll w = 1){ G[a].emplace_back(a, b, w); G[b].emplace_back(b, a, w); } void add_arrow(int a, int b, ll w = 1){ G[a].emplace_back(a, b, w); } //Topological_sort //!!return empty, if not DAG vector topological_sort() const; //Dijkstra and related vector dijkstra(ll s, bool restore = false) const; vector shortest_path(ll start, ll goal) const; //Bellman-Ford //!!return empty, if negative loop exists vector bellman_ford(ll s) const; //Warshall-Floyd vector> Warshall_Floyd() const; //Kruskal //!!Required UnionFind Graph Kruskal() const; //Tree Algorithms //Tree centroid vector treeCentroid() const; }; vector Graph::dijkstra(ll s, bool restore) const{ vector dist(G.size(), INF); priority_queue, vector>, greater>> que; dist[s] = 0; que.emplace(dist[s], s); vector prev(G.size(), -1); while(!que.empty()){ ll cost, idx; tie(cost, idx) = que.top(); que.pop(); if(dist[idx] < cost) continue; for(auto &e : G[idx]){ auto next_cost = cost + e.weight; if(dist[e.to] <= next_cost) continue; dist[e.to] = next_cost; if(restore) prev[e.to] = e.from; que.emplace(dist[e.to], e.to); } } if(restore) return prev; return dist; } vector Graph::shortest_path(ll start, ll goal) const{ vector prev = dijkstra(start, true); vector path; for (int cur = goal; cur != -1; cur = prev[cur]) path.push_back(cur); reverse(path.begin(), path.end()); if (path.front() != start) return {}; return path; } vector Graph::bellman_ford(ll s) const{ vector dist(G.size(), INF); dist[s] = 0; for (ll i = 0; i < G.size(); ++i) { for (ll j = 0; j < G.size(); ++j){ for (auto& e : G[j]) { if(dist[e.from] == INF) continue; bool res = chmin(dist[e.to], dist[e.from] + e.weight); if (i == G.size() - 1 and res) return {}; } } } return dist; } vector> Graph::Warshall_Floyd() const { int N = G.size(); vector> d(N, vector(N)); rep(i, N) rep(j, N) { if (i == j) d[i][j] = 0; else d[i][j] = INF; } rep(i, N) for (auto &e : G[i]) d[i][e.to] = e.weight; rep(k, N) rep(i, N) rep(j, N) { if (d[i][k] == INF or d[k][j] == INF) continue; d[i][j] = min(d[i][j], d[i][k]+d[k][j]); } return d; } vector Graph::topological_sort() const{ vector ans; int N = G.size(); vector ind(N); rep(i, N) for (auto &e : G[i]) ind[e.to]++; queue que; rep(i, N) if (!ind[i]) que.push(i); while(!que.empty()){ int now = que.front(); ans.pb(now); que.pop(); for(auto& e : G[now]) { ind [e.to]--; if(!ind[e.to]) que.push(e.to); } } if (ans.size() != N) return {}; return ans; } vector Graph::treeCentroid() const{ int N = G.size(); vector centroid, val(N); auto dfs = [&](auto&& self, int cur, int par)->void { bool is_centroid = true; val[cur] = 1; for(auto &e : G[cur]){ if(e.to == par) continue; self(self, e.to, cur); val[cur] += val[e.to]; if(val[e.to] > N / 2) is_centroid = false; } if(N - val[cur] > N / 2) is_centroid = false; if(is_centroid) centroid.push_back(cur); }; dfs(dfs, 0, -1); return centroid; } // #include // using namespace atcoder; constexpr long long MOD = 1000000007; /*------------------------------- Main Code Here -----------------------------------------*/ int main() { ll N; cin >> N; vector

X(N - 1); cin >> X; Graph G(N); for(auto [a, b] : X){ --a, --b; G.add_edge(a, b); } auto ret = G.treeCentroid(); set st; auto dfs = [&](auto &&self, ll d, ll cur, ll par = -1, ll f = -1)->void { bool is_leaf = true; for(auto e : G[cur]){ if(e.to == par) continue; if(e.to == -1) continue; self(self, d + 1, e.to, e.from); is_leaf = false; } if(is_leaf) st.insert(d); }; if(len(ret) == 1){ dfs(dfs, 0, ret[0], -1, -1); drop(len(st) == 1 ? "Yes" : "No"); } drop("No"); return 0; }