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.
// "static void main" must be defined in a public class.
import java.util.*;
import java.io.*;
public class Main {
     static class FastReader{
        StringTokenizer st;
        BufferedReader br;
        public FastReader(){
            br = new BufferedReader( new InputStreamReader( System.in));
        }
        
        public int nextInt(){
            while( st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer( br.readLine() );
                }
                catch(IOException e){
                    e.printStackTrace();
                }
            }
            return Integer.parseInt(st.nextToken());
        }
    }
    public static void main(String[] args) {
        FastReader f = new FastReader();
        int n = f.nextInt();
        ArrayList< ArrayList<Integer> > tree = new ArrayList< ArrayList<Integer> >();
        for(int i = 0; i < n;i++)
            tree.add( new ArrayList<Integer>() );
        for(int i = 0; i < n - 1;i++){
            int u = f.nextInt() - 1, v = f.nextInt() - 1;
            tree.get( u ).add( v );
            tree.get( v ).add( u );            
        }
        System.out.println( getCount(tree) );
    }

    public static long getCount( ArrayList< ArrayList<Integer> > tree ){
        int n = tree.size();
        long[] ansForEachNode = new long[n];
        int[] countOfChildren = new int[n];
        ansForEachNode[0] = DFS1(0, -1, tree, countOfChildren);
        DFS2(0, -1, tree, countOfChildren, ansForEachNode);
        long max = 0;
        for(long elem : ansForEachNode)
            max = Math.max(elem, max);
        // trace(ansForEachNode);
        return max;
    }
    
    public static long DFS1(int root, int parent, ArrayList< ArrayList<Integer> > tree, int[] childrenCount){
        long ans = 0;
        int count = 1;
        for(int child : tree.get(root)){
            if(child == parent)
                continue;
            ans += DFS1(child, root, tree, childrenCount);
            count += childrenCount[child];
        }
        childrenCount[root] = count;
        return ans + count;
    }

    public static void DFS2(int root, int parent, ArrayList< ArrayList<Integer> > tree, int[] childrenCount, long[] ansForEachNode){
        for(int child : tree.get(root)){
            if(child == parent)
                continue;
            ansForEachNode[child] = ansForEachNode[root] - 2 *childrenCount[child] + childrenCount.length;
            DFS2(child, root, tree, childrenCount, ansForEachNode);            
        }
    }
    
    public static void trace( long ...args){
        for(long elem : args)
            System.out.print(elem + " ");
        System.out.println();
    }
}