Codeforces573C. Bear and Drawing

#include<bits/stdc++.h>
const int maxn=1e5+15;
using namespace std;
vector<int> g[maxn];
int n,leg[maxn];
bool mark[maxn];
void init(){
    scanf("%d",&n);
    for (int u,v,i=1;i<n;++i){
        scanf("%d%d",&u,&v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
}
void dfs(int u,int f){
    if (g[u].size()<=2){
        mark[u]=1;
        for (int i=0;i<g[u].size();++i)
            if (g[u][i]!=f) dfs(g[u][i],u);
    }
}
void work(){
    for (int i=1;i<=n;++i)
        if (g[i].size()==1) dfs(i,0);
    for (int u=1;u<=n;++u) if (!mark[u])
        for (int i=0;i<g[u].size();++i) if (mark[g[u][i]])
            ++leg[u];
    for (int u=1;u<=n;++u) if (!mark[u]){
        int cnt=0;
        for (int i=0;i<g[u].size();++i) if (!mark[g[u][i]])
            if (g[g[u][i]].size()>min(leg[g[u][i]],2)+1) ++cnt;
        if (cnt>2){puts("No");return;}
    }
    puts("Yes");
}
int main(){
    init();
    work();
    return 0;
}