//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};
void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};
template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());

int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  vector<vector<ll>>g(n);
  rep(i,0,n-1){
    ll u,v;cin>>u>>v;u--;v--;
    g[u].PB(v);
    g[v].PB(u);
  }
  rep(i,0,n){
    if(g[i].size()&1)res++;
  }
  ll ok=n,ng=0;
  while(ok-ng>=2){
    ll mid=(ok+ng)/2;
    bool sw=true;
    auto dfs=[&](auto &&f,ll k,ll par)->ll{
      vector<ll>v;
      if(g[k].size()&1)v.PB(0);
      for(auto to:g[k]){
        if(to==par)continue;
        ll p=f(f,to,k);
        if(p!=-1)v.PB(p);
      }
      sort(ALL(v));
      ll sz=v.size();
      //cout<<k<<endl;
      //debug(v,sz);
      rep(i,0,sz/2){
        //cout<<i spa sz-i-1-(sz&1) spa v[i] spa v[sz-i-1-(sz&1)]<<endl;
        if(v[i]+v[sz-i-1-(sz&1)]>mid)sw=false;
      }
      if(sz%2==0){
        return -1;
      }
      else{
        ll ok=sz-1,ng=-1;
        while(ok-ng>=2){
          ll mid2=(ok+ng)/2;
          vector<ll>tmp;
          rep(i,0,sz)if(i!=mid2)tmp.PB(v[i]);
          bool sw2=true;
          rep(i,0,sz/2){
            //cout<<i spa sz-i-2 spa tmp[i] spa tmp[sz-i-2]<<endl;
            if(tmp[i]+tmp[sz-i-2]>mid)sw2=false;
          }
          if(sw2)ok=mid2;
          else ng=mid2;
        }
        return v[ok]+1;
      }
    };
    dfs(dfs,0,-1);
    if(sw)ok=mid;
    else ng=mid;
  }
  cout<<res/2 spa ok<<endl;
  return 0;
}

Measured memory_bytes: 21892