Problem:
Score : 900 points

Problem Statement

We have a tree with N vertices.
The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i.
For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.

It is expected that one of the vertices will be invaded by aliens from outer space.
Snuke wants to immediately identify that vertex when the invasion happens.
To do so, he has decided to install an antenna on some vertices.

First, he decides the number of antennas, K (1 ≤ K ≤ N).
Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively.
If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v).
Based on these K outputs, Snuke will identify the vertex that is invaded.
Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:

For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.

Find the minumum value of K, the number of antennas, when the condition is satisfied.

Constraints

2 ≤ N ≤ 10^5

0 ≤ a_i, b_i < N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}

Output

Print the minumum value of K, the number of antennas, when the condition is satisfied.

Sample Input 1

5
0 1
0 2
0 3
3 4

Sample Output 1

2

For example, install an antenna on Vertex 1 and 3.
Then, the following five vectors are distinct:

(d(1, 0), d(3, 0)) = (1, 1)

(d(1, 1), d(3, 1)) = (0, 2)

(d(1, 2), d(3, 2)) = (2, 2)

(d(1, 3), d(3, 3)) = (2, 0)

(d(1, 4), d(3, 4)) = (3, 1)

Sample Input 2

2
0 1

Sample Output 2

1

For example, install an antenna on Vertex 0.

Sample Input 3

10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8

Sample Output 3

3

For example, install an antenna on Vertex 0, 4, 9.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define fr(i,n) for(int i=0;i<(n);++i)
#define foor(i,a,b) for(int i=(a);i<=(b);++i)
#define rf(i,n) for(int i=(n);i--;)
#define roof(i,b,a) for(int i=(b);i>=(a);--i)
#define elsif else if
#define all(x) x.begin(),x.end()
#define Sort(x) sort(all(x))
#define Reverse(x) reverse(all(x))
#define PQ priority_queue
#define NP(x) next_permutation(all(x))
#define M_PI 3.14159265358979323846
#define popcount __builtin_popcount
using namespace std;            typedef vector<bool> vb; typedef vector<vb>  vvb;
                                typedef vector<int>  vi; typedef vector<vi>  vvi;
typedef long long ll;           typedef vector< ll>  vl; typedef vector<vl>  vvl;
typedef unsigned long long ull; typedef vector<ull>  vu; typedef vector<vu>  vvu;
typedef double dbl;             typedef vector<dbl>  vd; typedef vector<vd>  vvd;
typedef string str;             typedef vector<str>  vs; typedef vector<vs>  vvs;
typedef pair<int,int>pii;       typedef vector<pii>vpii; typedef map<int,int>mii;
typedef pair< ll, ll>pll;       typedef vector<pll>vpll; typedef map< ll, ll>mll;
typedef pair<dbl,dbl>pdd;       typedef vector<pdd>vpdd; typedef map<dbl,dbl>mdd;
typedef pair<str,str>pss;       typedef vector<pss>vpss; typedef map<str,str>mss;
typedef pair<int, ll>pil;       typedef vector<pil>vpil; typedef map<int, ll>mil;
typedef pair< ll,int>pli;       typedef vector<pli>vpli; typedef map< ll,int>mli;
typedef pair<dbl,int>pdi;       typedef vector<pdi>vpdi; typedef map<dbl,int>mdi;
template<typename T>vector<T>&operator<<(vector<T>&v,const T t){v.push_back(t);return v;}
template<typename T>multiset<T>&operator<<(multiset<T>&m,const T t){m.insert(t);return m;}
template<typename T>set<T>&operator<<(set<T>&s,const T t){s.insert(t);return s;}
template<typename T>stack<T>&operator<<(stack<T>&s,const T t){s.push(t);return s;}
template<typename T>stack<T>&operator>>(stack<T>&s,T&t){t=s.top();s.pop();return s;}
template<typename T>queue<T>&operator<<(queue<T>&q,const T t){q.push(t);return q;}
template<typename T>queue<T>&operator>>(queue<T>&q,T&t){t=q.front();q.pop();return q;}
template<typename T,typename U>PQ<T,vector<T>,U>&operator<<(PQ<T,vector<T>,U>&q,const T t){q.push(t);return q;}
template<typename T,typename U>PQ<T,vector<T>,U>&operator>>(PQ<T,vector<T>,U>&q,T&t){t=q.top();q.pop();return q;}
template<typename T,typename U>istream&operator>>(istream&s,pair<T,U>&p){return s>>p.first>>p.second;}
istream&operator>>(istream&s,_Bit_reference b){int a;s>>a;assert(a==0||a==1);b=a;return s;}
template<typename T>istream&operator>>(istream&s,vector<T>&v){fr(i,v.size()){s>>v[i];}return s;}
template<typename T,typename U>ostream&operator<<(ostream&s,const pair<T,U>p){return s<<p.first<<" "<<p.second;}
//template<typename T>ostream&operator<<(ostream&s,const vector<T>v){for(auto a:v){s<<a<<"\n";}return s;}
template<typename T>ostream&operator<<(ostream&s,const vector<T>v){fr(i,v.size()){i?s<<" "<<v[i]:s<<v[i];}return s;}
template<typename T>ostream&operator<<(ostream&s,const deque<T>d){fr(i,d.size()){i?s<<" "<<d[i]:s<<d[i];}return s;}
template<typename T>_Bit_reference operator&=(_Bit_reference b,T t){return b=b&t;}
template<typename T>_Bit_reference operator^=(_Bit_reference b,T t){return b=b^t;}
template<typename T>_Bit_reference operator|=(_Bit_reference b,T t){return b=b|t;}
template<typename T,typename U>pair<T,U>operator+(pair<T,U>a,pair<T,U>b){return {a.first+b.first,a.second+b.second};}
template<typename T,typename U>pair<T,U>operator-(pair<T,U>a,pair<T,U>b){return {a.first-b.first,a.second-b.second};}
template<typename T,typename U>pair<T,U>&operator+=(pair<T,U>&a,pair<T,U>b){return a=a+b;}
template<typename T,typename U>pair<T,U>&operator-=(pair<T,U>&a,pair<T,U>b){return a=a-b;}
void print(void){cout<<"\n";}
void Print(void){cout<<endl;}
template<typename T>void print(T t){cout<<t<<"\n";}
template<typename T>void Print(T t){cout<<t<<endl;}
template<typename T,typename...U>void print(T&&t,U&&...u){cout<<t<<" ";print(forward<U>(u)...);}
template<typename T,typename...U>void Print(T&&t,U&&...u){cout<<t<<" ";Print(forward<U>(u)...);}
bool YN(bool b){print(b?"YES":"NO");return b;}bool PI(bool b){print(b?"POSSIBLE":"IMPOSSIBLE");return b;}
bool Yn(bool b){print(b?"Yes":"No");return b;}bool Pi(bool b){print(b?"Possible":"Impossible");return b;}
bool yn(bool b){print(b?"yes":"no");return b;}bool pi(bool b){print(b?"possible":"impossible");return b;}
const int e5=1e5;
const int e9=1e9;
const int MD=1e9+7;
const int md=998244353;
const ll e18=1e18;
template<typename T>str to_string(const T&n){ostringstream s;s<<n;return s.str();}
template<typename T>T&chmax(T&a,T b){return a=max(a,b);}
template<typename T>T&chmin(T&a,T b){return a=min(a,b);}
template<typename T,typename U>vector<pair<T,U>>dijkstra(const vector<vector<pair<T,U>>>&E,const U s,const T inf){using P=pair<T,U>;vector<P>d;fr(i,E.size()){d<<P{inf,i};}PQ<P,vector<P>,greater<P>>pq;pq<<(d[s]=P{0,s});while(pq.size()){P a=pq.top();pq.pop();U v=a.second;if(d[v].first>=a.first){for(P e:E[v]){if(d[v].first+e.first<d[e.second].first){d[e.second]=P{d[v].first+e.first,v};pq<<P{d[v].first+e.first,e.second};}}}}return d;}
template<typename T,typename U>map<U,pair<T,U>>dijkstra(map<U,vector<pair<T,U>>>E,const U s,const T inf){using P=pair<T,U>;map<U,P>d;for(pair<U,vector<P>>e:E){d[e.first]=P{inf,e.first};}PQ<P,vector<P>,greater<P>>pq;pq<<(d[s]=P{0,s});while(pq.size()){P a=pq.top();pq.pop();U v=a.second;if(d[v].first>=a.first){for(P e:E[v]){if(d[v].first+e.first<d[e.second].first){d[e.second]=P{d[v].first+e.first,v};pq<<P{d[v].first+e.first,e.second};}}}}return d;}
ll maxflow(vector<mil>&E,int s,int t){ll z=0;vi b(E.size(),-1);for(int i=0;;++i){static auto dfs=[&](int v,ll f,auto&dfs)->ll{if(v==t)return f;b[v]=i;for(auto&p:E[v]){if(b[p.first]<i&&p.second){if(ll r=dfs(p.first,min(f,p.second),dfs)){p.second-=r;E[p.first][v]+=r;return r;}}}return 0;};ll x=dfs(s,ll(1e18),dfs);z+=x;if(x==0)return z;}}
template<typename T>T distsq(pair<T,T>a,pair<T,T>b){return (a.first-b.first)*(a.first-b.first)+(a.second-b.second)*(a.second-b.second);}
template<typename T>T max(const vector<T>a){assert(a.size());T m=a[0];for(T e:a){m=max(m,e);}return m;}
template<typename T>T min(const vector<T>a){assert(a.size());T m=a[0];for(T e:a){m=min(m,e);}return m;}
template<typename T>T gcd(const T a,const T b){return a?gcd(b%a,a):b;}
template<typename T>T gcd(const vector<T>a){T g=a[0];for(T e:a){g=gcd(g,e);}return g;}
template<typename T>vector<T>LIS(const vector<T>A){vector<T>B;for(T a:A){auto it=lower_bound(all(B),a);if(it==B.end()){B<<a;}else{*it=a;}}return B;}
template<typename T>vector<T>LCS(vector<T>A,vector<T>B){int N=A.size(),M=B.size();vector<vector<pair<int,pii>>>d(N+1,vector<pair<int,pii>>(M+1));fr(i,N){fr(j,M){if(A[i]==B[j]){d[i+1][j+1]={d[i][j].first+1,{i,j}};}else{d[i+1][j+1]=max(d[i][j+1],d[i+1][j]);}}}vector<T>r;for(pii p={N,M};d[p.first][p.second].first;p=d[p.first][p.second].second){r<<A[d[p.first][p.second].second.first];}Reverse(r);return r;}
str LCS(str S,str T){vector<char>s=LCS(vector<char>(S.begin(),S.end()),vector<char>(T.begin(),T.end()));return str(s.begin(),s.end());}
template<typename T>vector<pair<T,T>>ConvexHull(vector<pair<T,T>>V){if(V.size()<=3){return V;}Sort(V);rf(i,V.size()-1)V<<V[i];vector<pair<T,T>>r;for(pair<T,T>p:V){int s=r.size();while(s>=2&&(p.second-r[s-1].second)*(p.first-r[s-2].first)<(p.second-r[s-2].second)*(p.first-r[s-1].first)){r.pop_back();--s;}r<<p;}r.pop_back();return r;}
class UnionFind{vi p,s;void extend(int N){foor(i,p.size(),N){p<<i;s<<1;}}public:UnionFind(void){}UnionFind(int N){extend(N-1);}int find(int i){extend(i);return p[i]=p[i]==i?i:find(p[i]);}void unite(int a,int b){extend(a);extend(b);if((a=find(a))!=(b=find(b))){if(s[a]>s[b]){swap(a,b);}s[b]+=s[a];p[a]=b;}}void unite(pii p){return unite(p.first,p.second);}bool same(int a,int b){extend(a);extend(b);return find(a)==find(b);}bool same(pii p){return same(p.first,p.second);}int size(int x){extend(x);return s[find(x)];}};
ll MST(vector<pair<ll,pii>>&E){Sort(E);UnionFind uf;ll z=0;for(auto&e:E){if(!uf.same(e.second)){z+=e.first;uf.unite(e.second);}}return z;}
ll strmod(const str&s,const int m){ll x=0;fr(i,s.size()){x=(x*10+s[i]-48)%m;}return x;}
vvl mul(const vvl&A,const vvl&B,const int m){vvl C;fr(y,A.size()){C<<vl(B[y].size());}fr(y,C.size()){fr(x,C[y].size()){fr(i,A[0].size()){(C[y][x]+=A[y][i]*B[i][x])%=m;}}}return C;}
vvl pow(const vvl&A,const ll n,const int m){vvl B;fr(y,A.size()){B<<vl(A.size());}if(n==0){fr(i,B.size()){B[i][i]=1;}}elsif(n%2){B=mul(A,pow(A,n-1,m),m);}else{vvl C=pow(A,n/2,m);B=mul(C,C,m);}return B;}
ll pow(const ll a,const ll n,const int m){ll t;return n?(n&1?a>=0?a%m:(m-(-a%m))%m:1)*(t=pow(a,n>>1,m),t*t%m)%m:!!a;}
ll inv(const ll x,const int p){assert(x!=0);return pow(x,p-2,p);}
ll inv(const ll x){return inv(x,MD);}
vpll fact(const int n,const int p){assert(n<p);vpll v(n+1);v[0].first=1;foor(i,1,n){v[i].first=v[i-1].first*i%p;}v[n].second=inv(v[n].first,p);roof(i,n,1){v[i-1].second=v[i].second*i%p;}return v;}
class Combination{const vpll f;const int M;public:Combination(int n,int m):f(fact(n,m)),M(m){}Combination(int n):Combination(n,MD){}ll P(int n,int k){return n<0||k<0||n<k?0ll:f[n].first*f[n-k].second%M;}ll C(int n,int k){return k<0?0:P(n,k)*f[k].second%M;}ll H(int n,int k){return n==0&&k==0?1ll:C(n+k-1,k);}ll F(int n){return n<0?0:f[n].first;}};
ll C2(const int n){return(ll)n*~-n/2;}
ll sum(const vi a){ll s=0;for(int e:a){s+=e;}return s;}
ll sum(const vl a){ll s=0;for(ll e:a){s+=e;}return s;}
template<typename T>int MSB(T N){int r=-1;for(;N>0;N/=2){++r;}return r;}
template<typename T>class SegmentTree{vector<T>S;T(*const op)(T a,T b);const T zero;const int B;public:SegmentTree(int N,T(*f)(T a,T b),const T zero):S(1<<MSB(N-1)+2,zero),op(f),zero(zero),B(1<<MSB(N-1)+1){}SegmentTree(vector<T>v,T(*f)(T a,T b),const T zero):SegmentTree(v.size(),f,zero){fr(i,v.size()){S[S.size()/2+i]=v[i];}roof(i,S.size()/2-1,1){S[i]=op(S[i*2],S[i*2+1]);}}T calc(int l,int r){l+=B;r+=B;if(l>r){return zero;}if(l==r){return S[l];}T L=S[l],R=S[r];for(;l/2<r/2;l/=2,r/=2){if(l%2==0){L=op(L,S[l+1]);}if(r%2==1){R=op(S[r-1],R);}}return op(L,R);}void replace(int i,T x){for(S[i+=B]=x;i!=1;i/=2){if(i%2){S[i/2]=op(S[i-1],S[i]);}else{S[i/2]=op(S[i],S[i+1]);}}}void add(int i,T x){replace(i,op(S[B+i],x));}T top(){return S[1];}T get(int i){return S[i+B];}};
ll BITsum(vl&B,int i){ll z=0;while(i>0){z+=B[i];i-=i&-i;}return z;}
void BITadd(vl&B,int i,ll x){while(i<B.size()){B[i]+=x;i+=i&-i;}}
ll fib(const ll n,const int m){ll a,b,c,d,A,B,C,D;a=1;b=0;c=0;d=1;rf(i,63){A=a*a+b*c;B=a*b+b*d;C=c*a+d*c;D=c*b+d*d;if(n>>i&1){a=A;b=B;c=C;d=D;A=a+b;B=a;C=c+d;D=c;}a=A%m;b=B%m;c=C%m;d=D%m;}return b;}
vi primes(int n){vb b(n+1);vi p;foor(i,2,n){if(!b[i]){p<<i;for(int j=2*i;j<=n;j+=i){b[j]=true;}}}return p;}
vb isprime(const int n){vb v(n+1,true);v[0]=v[1]=false;foor(i,2,n){if(v[i]){for(int j=2*i;j<=n;j+=i){v[j]=false;}}}return v;}
class LCA{vvi par;vi dep;public:LCA(vvi&E,int root):par(MSB(E.size())+1,vi(E.size())),dep(E.size()){function<void(int,int)>dfs=[&](int i,int p){for(int j:E[i])if(j!=p){par[0][j]=i;dep[j]=dep[i]+1;dfs(j,i);}};par[0][root]=root;dfs(root,root);fr(i,par.size()-1){fr(j,par[0].size()){par[i+1][j]=par[i][par[i][j]];}}}int operator()(int a,int b){if(dep[a]>dep[b])swap(a,b);for(int t=dep[b]-dep[a],i=0;t;t>>=1,++i){if(t&1){b=par[i][b];}}if(a==b)return a;rf(i,par.size()){if(par[i][a]!=par[i][b]){a=par[i][a];b=par[i][b];}}return par[0][a];}};
vpli factor(ll N){vpli r;for(ll i=2;i*i<=N;++i){if(N%i==0){r<<pli{i,0};while(N%i==0){N/=i;++r.back().second;}}}if(N>1){r<<pli{N,1};}return r;}
vl divisors(ll n){vl r;ll m=sqrt(n);foor(i,1,m)if(n%i==0)r<<ll(i);rf(i,r.size()-(m*m==n))r<<n/r[i];return r;}
vi SuffixArray(str S){int N=S.size();vi rank(N+1),tmp(N+1),sa(N+1);fr(i,N){sa[i]=i;rank[i]=S[i];}sa[N]=N;rank[N]=-1;int k;auto cmp=[&](int&a,int&b)->bool{if(rank[a]!=rank[b])return rank[a]<rank[b];return (a+k<=N?rank[a+k]:-1)<(b+k<=N?rank[b+k]:-1);};for(k=1;k<=N;k*=2){sort(all(sa),cmp);tmp[sa[0]]=0;foor(i,1,N){tmp[sa[i]]=tmp[sa[i-1]]+cmp(sa[i-1],sa[i]);}rank=tmp;}return sa;};

int main(){cin.tie(0);ios::sync_with_stdio(false);
	int N;cin>>N;
	vvi E(N);
	fr(i,N-1){
		int a,b;cin>>a>>b;
		E[a]<<b;
		E[b]<<a;
	}
	function<int(int,int)>f=[&](int i,int p){
		int x=0;
		bool b=false;
		for(int j:E[i])if(j!=p){
			int t=f(j,i);
			x+=t;
			x+=b&&!t;
			b|=!t;
		}
		return x;
	};
	fr(i,N)if(E[i].size()==1){
		print(f(i,i)+1);
		break;
	}
	return 0;
}