#include using namespace std; using ll = long long; using ull = unsigned long long; #define ALL(obj) (obj).begin(),(obj).end() #define SPEED cin.tie(0);ios::sync_with_stdio(false); template using PQ = priority_queue; template using PQR = priority_queue,greater>; constexpr long long MOD = (long long)1e9 + 7; constexpr long long MOD2 = 998244353; constexpr long long HIGHINF = (long long)1e18; constexpr long long LOWINF = (long long)1e15; constexpr long double PI = 3.1415926535897932384626433; template vector multivector(size_t N,T init){return vector(N,init);} template auto multivector(size_t N,T... t){return vector(N,multivector(t...));} template void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}} template ostream &operator<<(ostream &o, const map&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;} template ostream &operator<<(ostream &o, const set&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} template ostream &operator<<(ostream &o, const multiset&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} template ostream &operator<<(ostream &o, const vector&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} template ostream &operator<<(ostream &o, const pair&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;} void print(void) {cout << endl;} template void print(Head&& head) {cout << head;print();} template void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward(tail)...);} template void chmax(T& a, const T b){a=max(a,b);} template void chmin(T& a, const T b){a=min(a,b);} void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;} void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;} void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;} template class Tree { public: int nodeNum; int isWeighted; int maxBit; int idx; vector> edge; vector> weight; vector depth; vector order; vector dist; vector parent; vector parentDist; vector> child; vector> childDist; vector> ancestor; vector> descendant; vector eulerTour; vector eulerTourDist; vector eulerTourIdxL; vector eulerTourIdxR; vector eulerTourDive,eulerTourFloat; vector eulerTourDiveDist,eulerTourFloatDist; vector eulerTourDiveIdxL,eulerTourFloatIdxL; vector eulerTourDiveIdxR,eulerTourFloatIdxR; Tree(const int nodeNum, const int isWeighted = 0, const int maxBit = 20) : nodeNum(nodeNum), isWeighted(isWeighted), maxBit(maxBit), edge(nodeNum), depth(nodeNum), order(nodeNum) { if(isWeighted) weight.resize(nodeNum); if(isWeighted) dist.resize(nodeNum); } //O(1) anytime void makeEdge(const int& from, const int& to, const T& w = 0) { edge[from].push_back(to); if(isWeighted) weight[from].push_back(w); } //O(N) anytime void makeDepth(const int root) { depth[root] = 0; if(isWeighted) dist[root] = 0; idx = 0; dfs1(root); order[idx++] = root; } //for makeDepth void dfs1(int from, int prev = -1){ for(int i = 0; i < edge[from].size(); ++i){ int to = edge[from][i]; if(to==prev) continue; depth[to] = depth[from] + 1; if(isWeighted) dist[to] = dist[from] + weight[from][i]; dfs1(to,from); order[idx++] = to; } } //O(N) anytime int diameter(void){ makeDepth(0); int tmp = max_element(depth.begin(), depth.end()) - depth.begin(); makeDepth(tmp); return *max_element(depth.begin(), depth.end()); } //O(N) after makeDepth void makeParent(void) { parent.resize(nodeNum); iota(parent.begin(),parent.end(),0); for (int i = 0; i < nodeNum; ++i) for (auto j : edge[i]) if (depth[i] > depth[j]) parent[i] = j; if(isWeighted) { parentDist.resize(nodeNum); for (int i = 0; i < nodeNum; ++i) for (int j = 0; j < edge[i].size(); ++j) if (depth[i] > depth[edge[i][j]]) parentDist[i] = weight[i][j]; } } //O(N) after makeDepth void makeChild(void) { child.resize(nodeNum); for (int i = 0; i < nodeNum; ++i) for (auto j : edge[i]) if (depth[i] < depth[j]) child[i].push_back(j); if(isWeighted) { childDist.resize(nodeNum); for (int i = 0; i < nodeNum; ++i) for (int j = 0; j < edge[i].size(); ++j) if (depth[i] < depth[edge[i][j]]) childDist[i].push_back(weight[i][j]); } } //O(NlogN) after makeDepth void makeAncestor(void) { ancestor.resize(nodeNum,vector(maxBit)); for (int i = 0; i < nodeNum; ++i) ancestor[i][0] = i; for (int i = 0; i < nodeNum; ++i) for (auto j : edge[i]) if (depth[i] > depth[j]) ancestor[i][0] = j; for (int bit = 1; bit < maxBit; ++bit) for (int i = 0; i < nodeNum; ++i) ancestor[i][bit] = ancestor[ancestor[i][bit - 1]][bit - 1]; } //O(N^2) after makeDepth void makeDescendant(void) { descendant.resize(nodeNum); for (int i = 0; i < nodeNum; ++i) descendant[i].push_back(i); for (int i = 0; i < nodeNum; ++i) for (auto j : edge[order[i]]) if (depth[order[i]] < depth[j]) for(auto k: descendant[j]) descendant[order[i]].push_back(k); } //O(logN) after makeAncestor int lca(int l, int r) { if (depth[l] < depth[r]) swap(l, r); int diff = depth[l] - depth[r]; for (int bit = 0; bit < maxBit; ++bit) if (diff & (1 << bit)) l = ancestor[l][bit]; if(l==r) return l; for (int bit = maxBit - 1; 0 <= bit; --bit) if(ancestor[l][bit]!=ancestor[r][bit]) l = ancestor[l][bit], r = ancestor[r][bit]; return ancestor[l][0]; } //O(N) after makeChild and makeParent void makeEulerTour(void){ dfs2(order[nodeNum-1]); eulerTourIdxL.resize(nodeNum); eulerTourIdxR.resize(nodeNum); for(int i = 0; i < eulerTour.size(); ++i) eulerTourIdxR[eulerTour[i]] = i; for(int i = eulerTour.size()-1; 0 <= i; --i) eulerTourIdxL[eulerTour[i]] = i; return; } //for makeEulerTour void dfs2(int from, int prev = -1){ eulerTour.push_back(from); if(isWeighted) eulerTourDist.push_back(parentDist[from]); for(int i = 0; i < child[from].size(); ++i){ int to = child[from][i]; dfs2(to,from); eulerTour.push_back(from); if(isWeighted) eulerTourDist.push_back(-childDist[from][i]); } } //O(NlogN) after makeEulerTour void makeEulerTourEdge(void) { eulerTourDive.push_back(order[nodeNum-1]); if(isWeighted) eulerTourDiveDist.push_back(0); for(int i = 1; i < eulerTour.size(); ++i) { int l = eulerTour[i-1]; int r = eulerTour[i]; if(depth[l] < depth[r]) { eulerTourDive.push_back(i); if(isWeighted) eulerTourDiveDist.push_back(eulerTourDist[i]); } else { eulerTourFloat.push_back(i); if(isWeighted) eulerTourFloatDist.push_back(eulerTourDist[i]); } } eulerTourDiveIdxL.resize(nodeNum); eulerTourDiveIdxR.resize(nodeNum); eulerTourFloatIdxL.resize(nodeNum); eulerTourFloatIdxR.resize(nodeNum); for(int i = 0; i < nodeNum; ++i) { int l = eulerTourIdxL[i]; int r = eulerTourIdxR[i]; eulerTourDiveIdxL[i] = upper_bound(eulerTourDive.begin() ,eulerTourDive.end() ,l) - eulerTourDive.begin() ; eulerTourDiveIdxR[i] = (upper_bound(eulerTourDive.begin() ,eulerTourDive.end() ,r) - eulerTourDive.begin()) -1; eulerTourFloatIdxL[i] = upper_bound(eulerTourFloat.begin(),eulerTourFloat.end(),l) - eulerTourFloat.begin() ; eulerTourFloatIdxR[i] = (upper_bound(eulerTourFloat.begin(),eulerTourFloat.end(),r) - eulerTourFloat.begin()) -1; eulerTourDiveIdxR[i] = max(eulerTourDiveIdxL[i]-1 ,eulerTourDiveIdxR[i]); eulerTourFloatIdxR[i] = max(eulerTourFloatIdxL[i]-1,eulerTourFloatIdxR[i]); } } // iの部分木の頂点に加算するとき // [ eulerTourIdxL[i] ,eulerTourIdxR[i] ]に +val // [i]の頂点クエリ // [eulerTourIdxL[i],eulerTourIdxL[i]] // iの部分木の辺に加算するとき // [ eulerTourDiveIdxL[i] ,eulerTourDiveIdxR[i] ]に +val // [ eulerTourFloatIdxL[i] ,eulerTourFloatIdxR[i] ]に -val // [0,i]のパスクエリ // [ 0, eulerTourDiveIdxL[i] ) + [0, eulerTourFloatIdxL[i]) }; //depth,dist //https://atcoder.jp/contests/abc126/tasks/abc126_d //lca //https://atcoder.jp/contests/abc014/tasks/abc014_4 //child //https://atcoder.jp/contests/abc133/tasks/abc133_e //diameter //https://atcoder.jp/contests/agc033/tasks/agc033_c //eulerTour //https://yukicoder.me/problems/no/900 int main() { int N; cin >> N; Tree<> tree(N); corner(N==1,1); for(int i = 0; i < N-1; ++i){ int u,v; cin >> u >> v; u--,v--; tree.makeEdge(u,v); tree.makeEdge(v,u); } vector dp1(N,1),dp2(N,0); tree.makeDepth(0); tree.makeChild(); for(int pa:tree.order){ int sum0 = 0,sum1 = 0,sum2 = 0,m = tree.child[pa].size(); for(int& ch:tree.child[pa]) sum1 += dp1[ch]; for(int& ch:tree.child[pa]) sum2 += dp2[ch]; for(int& ch:tree.child[pa]) sum0 += max(dp1[ch],dp2[ch]); chmax(dp1[pa],sum1 - m + 1); chmax(dp1[pa],sum2 + 1); chmax(dp1[pa],sum0); chmax(dp2[pa],sum1); chmax(dp2[pa],sum2); chmax(dp2[pa],sum0); } cout << max(dp1[0],dp2[0]) << endl; return 0; }