You are given a tree (an undirected connected acyclic graph) consisting of n vertices. You are playing a game on this tree.

Initially all vertices are white. On the first turn of the game you choose one vertex and paint it black. Then on each turn you choose a white vertex adjacent (connected by an edge) to any black vertex and paint it black.

Each time when you choose a vertex (even during the first turn), you gain the number of points equal to the size of the connected component consisting only of white vertices that contains the chosen vertex. The game ends when all vertices are painted black.

Let's see the following example:

<image>

Vertices 1 and 4 are painted black already. If you choose the vertex 2, you will gain 4 points for the connected component consisting of vertices 2, 3, 5 and 6. If you choose the vertex 9, you will gain 3 points for the connected component consisting of vertices 7, 8 and 9.

Your task is to maximize the number of points you gain.

Input

The first line contains an integer n — the number of vertices in the tree (2 ≤ n ≤ 2 ⋅ 10^5).

Each of the next n - 1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the indices of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i).

It is guaranteed that the given edges form a tree.

Output

Print one integer — the maximum number of points you gain if you will play optimally.

Examples

Input


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


Output


36


Input


5
1 2
1 3
2 4
2 5


Output


14

Note

The first example tree is shown in the problem statement.
import java.util.*;
import java.io.*;
import java.text.*;
public class Main{
    //SOLUTION BEGIN
    //Into the Hardware Mode
    void pre() throws Exception{}
    void solve(int TC) throws Exception{
        int n = ni();
        int[][] e = new int[n-1][];
        for(int i = 0; i< n-1; i++)e[i] = new int[]{ni()-1, ni()-1};
        int[][] g = makeU(n, e);
        long[] a = new long[n], b = new long[n];
        int[] sub = new int[n];
        dfs(g, a,sub, 0, -1);
        dfs1(g, a, b, sub, 0, -1);
        long ans = 0;
        for(int i = 0; i< n; i++)ans = Math.max(ans, a[i]+b[i]);
        pn(ans);
    }
    void dfs1(int[][] g, long[] a, long[] b, int[] sub, int u, int p){
        int n = g.length;
        for(int v:g[u]){
            if(v == p)continue;
            b[v] = b[u]+n-sub[v]+a[u]-a[v]-sub[v];
            dfs1(g, a, b, sub, v, u);
        }
    }
    void dfs(int[][] g, long[] a, int[] sub, int u, int p){
        sub[u] = 1;
        for(int v:g[u]){
            if(v == p)continue;
            dfs(g, a, sub, v, u);
            a[u] += a[v];
            sub[u] += sub[v];
        }
        a[u] += sub[u];
    }
    int[][] makeU(int n, int[][] edge){
        int[][] g = new int[n][];int[] cnt = new int[n];
        for(int i = 0; i< edge.length; i++){cnt[edge[i][0]]++;cnt[edge[i][1]]++;}
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]];
        for(int i = 0; i< edge.length; i++){
            g[edge[i][0]][--cnt[edge[i][0]]] = edge[i][1];
            g[edge[i][1]][--cnt[edge[i][1]]] = edge[i][0];
        }
        return g;
    }
    //SOLUTION END
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    long IINF = (long)1e18, mod = (long)1e9+7;
    final int INF = (int)1e9, MX = (int)2e5+5;
    DecimalFormat df = new DecimalFormat("0.00000000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-6;
    static boolean multipleTC = false, memory = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        in = new FastReader();
        out = new PrintWriter(System.out);
        //Solution Credits: Taranpreet Singh
        int T = (multipleTC)?ni():1;
        pre();for(int t = 1; t<= T; t++)solve(t);
        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n()throws Exception{return in.next();}
    String nln()throws Exception{return in.nextLine();}
    int ni()throws Exception{return Integer.parseInt(in.next());}
    long nl()throws Exception{return Long.parseLong(in.next());}
    double nd()throws Exception{return Double.parseDouble(in.next());}

    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }

        String next() throws Exception{
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    throw new Exception(e.toString());
                }
            }
            return st.nextToken();
        }

        String nextLine() throws Exception{
            String str = "";
            try{   
                str = br.readLine();
            }catch (IOException e){
                throw new Exception(e.toString());
            }  
            return str;
        }
    }
}