#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC target ("avx2")
//#pragma GCC optimization ("unroll-loops")

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

const long double PI = 4*atan(1);

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;
typedef complex<ld> cd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define f1r(i,a,b) for (int i = (a); i < (b); ++i)
#define f0r(i,a) f1r(i,0,a)
#define trav(a, x) for (auto& a : x)
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)(x).size()
#define all(x) x.begin(), x.end()
#define rall(x) rbegin(x), rend(x)
#define resz resize
#define rsz resize
#define ins insert

template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) {
  cout << "["; for(int i = 0; i < v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "]"; }

template<class T> bool ckmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }

namespace input {
	template<class T> void re(complex<T>& x);
	template<class T1, class T2> void re(pair<T1,T2>& p);
	template<class T> void re(vector<T>& a);
	template<class T, size_t SZ> void re(array<T,SZ>& a);
	template<class T> void re(T& x) { cin >> x; }
	void re(double& x) { string t; re(t); x = stod(t); }
	void re(ld& x) { string t; re(t); x = stold(t); }
	template<class T, class... Ts> void re(T& t, Ts&... ts) {
		re(t); re(ts...); }
	template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
	template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
	template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
	template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
	void pr(int x) { cout << x; }
	void pr(long x) { cout << x; }
	void pr(ll x) { cout << x; }
	void pr(unsigned x) { cout << x; }
	void pr(unsigned long x) { cout << x; }
	void pr(unsigned long long x) { cout << x; }
	void pr(float x) { cout << x; }
	void pr(double x) { cout << x; }
	void pr(ld x) { cout << x; }
	void pr(char x) { cout << x; }
	void pr(const char* x) { cout << x; }
	void pr(const string& x) { cout << x; }
	void pr(bool x) { pr(x ? "true" : "false"); }
	template<class T> void pr(const complex<T>& x) { cout << x; }
	template<class T1, class T2> void pr(const pair<T1,T2>& x);
	template<class T> void pr(const T& x);
	template<class T, class... Ts> void pr(const T& t, const Ts&... ts) {
		pr(t); pr(ts...); }
	template<class T1, class T2> void pr(const pair<T1,T2>& x) {
		pr("{",x.f,", ",x.s,"}"); }
	template<class T> void pr(const T& x) {
		pr("{"); // const iterator needed for vector<bool>
		bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0;
		pr("}"); }
	void ps() { pr("\n"); } // print w/ spaces
	template<class T, class... Ts> void ps(const T& t, const Ts&... ts) {
		pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); }
	void pc() { pr("]\n"); } // debug w/ commas
	template<class T, class... Ts> void pc(const T& t, const Ts&... ts) {
		pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); }
	#ifdef TQIAN
	#define dbg(x...) pr("[",#x,"] = ["), pc(x);
	#else
	#define dbg(x...) 0
	#endif
}

using namespace output;

namespace io {
	void setIn(string s) { freopen(s.c_str(),"r",stdin); }
	void setOut(string s) { freopen(s.c_str(),"w",stdout); }
	void setIO(string s = "") {
		cin.sync_with_stdio(0); cin.tie(0); // fast I/O
		// cin.exceptions(cin.failbit); // ex. throws exception when you try to read letter into int
		if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
	}
}

using namespace io;
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());

const int MOD = 1e9 + 7;

typedef decay<decltype(MOD)>::type T;
struct mi {
	T val;
	explicit operator T() const { return val; }
	mi() { val = 0; }
	mi(const ll& v) {
		val = (-MOD <= v && v <= MOD) ? v : v % MOD;
		if (val < 0) val += MOD; }
    friend ostream& operator<<(ostream& os, const mi& a) { return os << a.val; }
	friend void pr(const mi& a) { pr(a.val); }
	friend void re(mi& a) { ll x; re(x); a = mi(x); }
	friend bool operator==(const mi& a, const mi& b) { return a.val == b.val; }
	friend bool operator!=(const mi& a, const mi& b) { return !(a == b); }
	friend bool operator<(const mi& a, const mi& b) { return a.val < b.val; }
	mi operator-() const { return mi(-val); }
	mi& operator+=(const mi& m) {
		if ((val += m.val) >= MOD) val -= MOD;
		return *this; }
	mi& operator-=(const mi& m) {
		if ((val -= m.val) < 0) val += MOD;
		return *this; }
	mi& operator*=(const mi& m) { val = (ll)val*m.val%MOD;
		return *this; }
	friend mi pow(mi a, ll p) {
		mi ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans; }
	friend mi inv(const mi& a) { assert(a != 0); return pow(a,MOD-2); }
	mi& operator/=(const mi& m) { return (*this) *= inv(m); }
	friend mi operator+(mi a, const mi& b) { return a += b; }
	friend mi operator-(mi a, const mi& b) { return a -= b; }
	friend mi operator*(mi a, const mi& b) { return a *= b; }
	friend mi operator/(mi a, const mi& b) { return a /= b; }
};

typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
const int MAX = 1e5 + 5;
int n; vector<vi> par, adj; vi depth;
void init(int _N) {
    n = _N;
    int d = 1; while ((1<<d) < n) d ++;
    par.assign(d,vi(n)); adj.resz(n); depth.resz(n);
}
void ae(int x, int y) { adj[x].pb(y), adj[y].pb(x); }
void dfs(int x = 0) {
    FOR(i,1,sz(par)) par[i][x] = par[i-1][par[i-1][x]];
    trav(y,adj[x]) if (y != par[0][x])
        depth[y] = depth[par[0][y] = x]+1, dfs(y);
}
void gen(int R = 0) { par[0][R] = R; dfs(R); }

int jmp(int x, int d) {
    F0R(i,sz(par)) if ((d>>i)&1) x = par[i][x];
    return x; }
int lca(int x, int y) {
    if (depth[x] < depth[y]) swap(x,y);
    x = jmp(x,depth[x]-depth[y]); if (x == y) return x;
    R0F(i,sz(par)) {
        int X = par[i][x], Y = par[i][y];
        if (X != Y) x = X, y = Y;
    }
    return par[0][x];
}
int dist(int x, int y) { // # edges on path
    return depth[x]+depth[y]-2*depth[lca(x,y)]; }
/// edges numbered 1 to n-1 inclusive
bool vis[MAX];
vi edges;
int ans = 1;
void dfs_vert(int src){
    if(sz(adj[src])%2 == 1) return;
    for(int nxt: adj[src]){
        /// src to nxt
        int val = (depth[src]<depth[nxt] ? nxt:src);
        if(vis[val]) continue;
        vis[val] = true;
        edges.eb(val);
        dfs_vert(nxt);
    }
}
int dep[MAX];
bool ok;
bool check_even(vi& v, int rid, int mx){
    int l = 0;
    int r = sz(v) - 1;
    while(l<=r){
        if(l == rid) l++;
        if(r == rid) r--;
        if(l>r) return true;
        if(v[l] + v[r]>mx) return false;
        l++; r--;
    }
    return true;
}
int solve_even(vi & legs, int mx){
    int lo = 0;
    int hi = sz(legs) - 1;
    while(hi-lo>1){
        int mid = (lo+hi)/2;
        if(check_even(legs, mid, mx)) hi = mid;
        else lo = mid+1;
    }
    if(check_even(legs, lo, mx)) return legs[lo];
    else if(check_even(legs, hi, mx)) return legs[hi];
    else{
        ok = false;
        return legs.back();
    }
}
int solve_odd(vi & legs, int mx){
    int l = 0;
    int r = sz(legs) - 1;
    bool good = true;
    while(l<=r){
        if(legs[l]+legs[r]>mx) {
            good = false; break;
        }
        l++; r--;
    }
    if(good) return 0;
    int id = -1;
    f0r(i, sz(legs)) if(legs[i]<=mx) id = i;
    if(id == -1){
        ok = false;
        return legs.back();
    }
    legs.erase(legs.begin()+id);
    return solve_even(legs, mx);
}
int root;
int dfs_solve(int src, int par, int mx){
    if(sz(adj[src]) == 1 && src != root) return 0;
    vi legs;
    for(int nxt: adj[src]){
        if(nxt == par) continue;
        legs.eb(dfs_solve(nxt, src, mx)+1);
    }
    sort(all(legs));
    if(legs.back()>mx){
        ok = false;
        return legs.back();
    }
    if(src == root){
        if(sz(adj[src])%2 == 0){
            int l = 0;
            int r = sz(legs)-1;
            while(l<=r){
                if(legs[l]+legs[r]>mx){
                    ok = false; break;
                }
                l++; r--;
            }
        }
        else{
            if(sz(adj[src]) == 1){
                if(legs.back()>mx) ok = false;
                return legs.back();
            }
            int id = -1;
            f0r(i, sz(legs)) if(legs[i]<=mx) id = i;
            if(id == -1){
                ok = false;
                return legs.back();
            }
            legs.erase(legs.begin()+id);
            int l = 0; int r = sz(legs)-1;
            while(l<=r){
                if(legs[l]+legs[r]>mx) {
                    ok = false; break;
                }
                l++; r--;
            }
        }
        return legs.back();

    }
    if(sz(adj[src])%2 == 0) return solve_even(legs, mx);
    else return solve_odd(legs, mx);
}
int main(){
    re(n);
    init(n);
    f0r(i, n-1){
        int u, v; re(u, v); u--; v--;
        ae(u, v);
    }
    gen();
    int ed = 0;
    f0r(i, n) if(sz(adj[i])%2 == 1) ed++;
    int a = ed/2;
    int lo = 1;
    int hi = MAX;
    root = 0;
    while(hi-lo>1){
        int mid = (lo+hi)/2;
        ok = true;
        dfs_solve(root, -1, mid);
        if(ok) hi = mid;
        else lo = mid+1;
    }
    ok = true;
    dfs_solve(root, -1, lo);
    if(ok) ckmax(ans, lo);
    else ckmax(ans, hi);
    ps(a, ans);
    return 0;
}


Measured memory_bytes: 26412