Tree Matching

/*
    author: kartik8800
*/
 
#include<bits/stdc++.h>
#define ll long long
#define pb push_back
#define fr(a,b) for(int i = a; i < b; i++)
#define rep(i,a,b) for(int i = a; i < b; i++)
#define mod 1000000007
#define inf (1LL<<60)
#define all(x) (x).begin(), (x).end()
#define prDouble(x) cout << fixed << setprecision(10) << x
#define triplet pair<ll,pair<ll,ll>>
#define fast_io ios_base::sync_with_stdio(false);cin.tie(NULL)
using namespace std;
 
vector<int> tree[200001];
int dp[200001][2];
 
void solve(int src, int par)
{
    vector<int> prefix, suffix;
    dp[src][0] = dp[src][1] = 0;
 
    bool leaf = 1;
    for(int child : tree[src])
    {
        if(child != par)
        {
            leaf = 0;
            solve(child, src);
        }
    }
 
    if(leaf)return;
    for(int child : tree[src])
    {
        if(child != par)
        {
            prefix.push_back(max(dp[child][0], dp[child][1]));
            suffix.push_back(max(dp[child][0], dp[child][1]));
        }
    }
 
    fr(1,(int)prefix.size())
        prefix[i] += prefix[i-1];
    for(int i = (int)suffix.size() - 2; i >= 0; i--)
        suffix[i] += suffix[i+1];
 
    dp[src][0] = suffix[0];
    int c_no = 0;
    for(int child : tree[src])
    {
        if(child == par)continue;
 
        int leftChildren = (c_no == 0) ? 0 : prefix[c_no - 1];
        int rightChildren = (c_no == (int)suffix.size() - 1) ? 0 : suffix[c_no + 1];
 
        dp[src][1] = max(dp[src][1], 1 + leftChildren + rightChildren + dp[child][0]);
        c_no++;
    }
}
 
int main() {
   fast_io;
   ll t,n,m,x,i,j,k,q;
   //cin >> t;
   t = 1;
   while(t--)
   {
        cin >> n;
        vector<int> ans(n+1);
        fr(2,n+1)
        {
            int u,v;
            cin >> u >> v;
            tree[u].push_back(v);
            tree[v].push_back(u);
        }
        solve(1, 0);
        cout << max(dp[1][0], dp[1][1]);
   }
   return 0;
}