Problem: Takahashi has decided to make a Christmas Tree for the Christmas party in AtCoder, Inc.

A Christmas Tree is a tree with N vertices numbered 1 through N and N-1 edges, whose i-th edge (1\leq i\leq N-1) connects Vertex a_i and b_i.

He would like to make one as follows:

* Specify two non-negative integers A and B.
* Prepare A Christmas Paths whose lengths are at most B. Here, a Christmas Path of length X is a graph with X+1 vertices and X edges such that, if we properly number the vertices 1 through X+1, the i-th edge (1\leq i\leq X) will connect Vertex i and i+1.
* Repeat the following operation until he has one connected tree:
* Select two vertices x and y that belong to different connected components. Combine x and y into one vertex. More precisely, for each edge (p,y) incident to the vertex y, add the edge (p,x). Then, delete the vertex y and all the edges incident to y.
* Properly number the vertices in the tree.



Takahashi would like to find the lexicographically smallest pair (A,B) such that he can make a Christmas Tree, that is, find the smallest A, and find the smallest B under the condition that A is minimized.

Solve this problem for him.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq a_i,b_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}


Output

For the lexicographically smallest (A,B), print A and B with a space in between.

Examples

Input

7
1 2
2 3
2 4
4 5
4 6
6 7


Output

3 2


Input

8
1 2
2 3
3 4
4 5
5 6
5 7
5 8


Output

2 5


Input

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


Output

3 4

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x...) do { cout << "\033[32;1m " << #x << " -> "; err(x); } while (0)
void err() { cout << "\033[39;0m" << endl; }
template<template<typename...> class T, typename t, typename... A>
void err(T<t> a, A... x) { for (auto v: a) cout << v << ' '; err(x...); }
template<typename T, typename... A>
void err(T a, A... x) { cout << a << ' '; err(x...); }
#else
#define dbg(...)
#endif
typedef long long ll;
typedef pair<int,int> pi;
typedef vector<int> vi;
template<class T> using vc=vector<T>;
template<class T> using vvc=vc<vc<T>>;
template<class T> void mkuni(vector<T>&v)
{
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}
template<class T>
void print(T x,int suc=1)
{
    cout<<x;
    if(suc==1) cout<<'\n';
    else cout<<' ';
}
template<class T>
void print(const vector<T>&v,int suc=1)
{
    for(int i=0;i<v.size();i++)
    print(v[i],i==(int)(v.size())-1?suc:2);
}
const int maxn=1e5+7;
vi G[maxn];
int ans2=0;
int cur;
bool ok;
int dfs(int u,int fa=-1)
{
    vi sonlen;
    for(auto v:G[u])if(v!=fa)
    {
        int ret=dfs(v,u);
        sonlen.push_back(ret+1);
    }
    if(fa==-1&&G[u].size()%2==0)
    {
        sort(sonlen.begin(),sonlen.end());
        for(int l=0,r=sonlen.size()-1;l<r;l++,r--)
            if(sonlen[l]+sonlen[r]>cur) ok=0;
        return 0;
    }
    if(sonlen.size()%2==0) sonlen.push_back(0);
    sort(sonlen.begin(),sonlen.end());
    int L=0,R=sonlen.size()-1,ret=-1;
    while(L<=R)
    {
        int mid=L+R>>1;
        bool yes=1;
        for(int l=0,r=sonlen.size()-1;l<r;l++,r--)
        {
            if(l==mid) l++;
            if(r==mid) r--;
            if(sonlen[l]+sonlen[r]>cur) yes=0;
        }
        if(yes){
            ret=mid;
            R=mid-1;
        }
        else L=mid+1;
    }
    if(ret==-1){
        ok=0;
        ret=0;    
    }
    return sonlen[ret];
}
int main()
{
    int n;
    cin>>n;
    for(int i=1,u,v;i<n;i++)
    {
        cin>>u>>v;
        G[u].push_back(v);
        G[v].push_back(u);
    }
    int ans1=0,odd=0;
    for(int i=1;i<=n;i++)
        if(G[i].size()&1) odd++;
    ans1=odd/2;
    int L=1,R=n-1,ans2=-1;
    while(L<=R)
    {
        cur=L+R>>1;
        ok=1;
        int ret=dfs(1);
        //dbg(cur,ok);
        if(ret>cur) ok=0;
        if(ok)
        {
            ans2=cur;
            R=cur-1;
        }
        else L=cur+1;
    }
    cout<<ans1<<" "<<ans2<<'\n';
}