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.io.*;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;


public class Main
{	
   static long mod=(long)(1e+9 + 7);
   //static long mod=(long)998244353;
   
   static int[] sieve;
   static ArrayList<Integer> primes;
   static PrintWriter out;
   static fast s;
   static StringBuilder fans;

   public static void dfs1(int start,long[] dist,long[] cnt,int[] visited,ArrayList<Integer>[] graph,int a[])
   {
   	if(visited[start]==1) return;
   	
   	visited[start]=1;
   	cnt[start]=a[start];
   	
   	for(int i=0;i<graph[start].size();i++)
   		{
   			int u=start;
   			int v=graph[start].get(i);
   			
   			if(visited[v]==0)
   				{
						dfs1(v,dist,cnt,visited,graph,a);
						dist[u]+=dist[v];
						cnt[u]+=cnt[v];
   				}
   		}
   	
   	dist[start]+=cnt[start];
   }
   
   public static void dfs2(int start,long[] dist,long[] cnt,long[] ans,int[] visited,ArrayList<Integer>[] graph,int a[],long prev,long prev1)
      {
      	if(visited[start]==1) return;
      	
      	visited[start]=1;
      	ans[start]=dist[start]+prev;
      	cnt[start]+=prev1;
      	
      	for(int i=0;i<graph[start].size();i++)
      		{
      			int u=start;
      			int v=graph[start].get(i);
      			
      			if(visited[v]==0)
      				{
			   			long contrib=ans[u]-(dist[v]+cnt[v])+(cnt[u]-cnt[v]);
			   			long contrib1=cnt[u]-cnt[v];
			   			dfs2(v,dist,cnt,ans,visited,graph,a,contrib,contrib1);
      				}
      			
      		}
      }
   public static void solve()
   {
   	int n=s.nextInt();
   	int a[]=new int[n+1];
   	long cnt[]=new long[n+1];
   	
   	for(int i=1;i<=n;i++) a[i]=1;
   	
   	ArrayList<Integer> graph[]=new ArrayList[n+1];
   	
     for(int i=1;i<=n;i++) graph[i]=new ArrayList<Integer>();
     
     long dis[]=new long[n+1]; 
     Arrays.fill(dis, 0);
     
     int visited[]=new int[n+1];
     
   	for(int i=1;i<=n-1;i++)
   		{
   			int u=s.nextInt();
   			int v=s.nextInt();
   			graph[u].add(v);
   			graph[v].add(u);
   		}
   	
   	long ans[]=new long[n+1];
   	
   	dfs1(1,dis,cnt,visited,graph,a);
   	Arrays.fill(visited, 0);	
   	dfs2(1,dis,cnt,ans,visited,graph,a,0,0);
   	
   	long max=Long.MIN_VALUE;
   	
   	for(int i=1;i<=n;i++) max=Math.max(max, ans[i]);
   	System.out.println(max);
   }
  
   public static void main(String[] args) throws java.lang.Exception
   {	  	
	     s = new fast();
	     out=new PrintWriter(System.out);
	     fans=new StringBuilder("");
		    
	     
	     int t=1;
	    
	     while(t>0)
	    	 {
	    		 solve();
	    		 t--;
	    	 }
	     //System.out.println(fans);
   }
  
 
 
static class fast {   
	
	    private InputStream i;
		private byte[]  buf = new byte[1024];
		private int curChar;
		
		private int numChars;
		
		//Return floor log2n
		public static long log2(long bits) // returns 0 for bits=0
			{
			    int log = 0;
			    if( ( bits & 0xffff0000 ) != 0 ) { bits >>>= 16; log = 16; }
			    if( bits >= 256 ) { bits >>>= 8; log += 8; }
			    if( bits >= 16  ) { bits >>>= 4; log += 4; }
			    if( bits >= 4   ) { bits >>>= 2; log += 2; }
			    return log + ( bits >>> 1 );
			}
		
		public static boolean next_permutation(int a[])
		   {
			   int i=0,j=0;int index=-1;	   
			   int n=a.length;
			   
			   for(i=0;i<n-1;i++)
				   if(a[i]<a[i+1]) index=i;
			   
			   if(index==-1) return false;
			   i=index;
 
			  
			   for(j=i+1;j<n && a[i]<a[j];j++);
 
			   int temp=a[i];
			   a[i]=a[j-1];
			   a[j-1]=temp;
			   	   
			   for(int p=i+1,q=n-1;p<q;p++,q--)
			   {
				   temp=a[p];
				   a[p]=a[q];
				   a[q]=temp;
			   }
			   
			   return true;
		   }
		   
		   
		public static void division(char ch[],int divisor)
		   {
			   int div=Character.getNumericValue(ch[0]); int mul=10;int remainder=0;
			   StringBuilder quotient=new StringBuilder("");
			   for(int i=1;i<ch.length;i++)
			   {
				   div=div*mul+Character.getNumericValue(ch[i]);	
				   if(div<divisor) {quotient.append("0");continue;}
				   quotient.append(div/divisor);
				   div=div%divisor;mul=10;
				   
			   } 
			   remainder=div;
			   while(quotient.charAt(0)=='0')quotient.deleteCharAt(0);	   
			   System.out.println(quotient+" "+remainder);	  
		   }
		
		public static void sieve(int size)
		{
			sieve=new int[size+1];
			
			primes=new ArrayList<Integer>();
			
			sieve[1]=1;
			
			for(int i=2;i*i<=size;i++)
			{
				if(sieve[i]==0)
				 {
					for(int j=i*i;j<size;j+=i) {sieve[j]=1;}
				 }
			}
			
			for(int i=2;i<=size;i++)
			{
				if(sieve[i]==0) primes.add(i);
			}
		}
		
		public static long pow(long n, long b, long MOD)
		   {
		       long x=1;long y=n; 
		       while(b > 0)
		       {
		           if(b%2 == 1)
		           {
		               x=x*y;
		               if(x>MOD) x=x%(MOD);
		           }
		           y = y*y;
		           if(y>MOD) y=y%(MOD); 
		           b >>= 1;
		       }
		       return x;
		   }
 
 
		public static long mod_inv(long n,long mod)
		{
			return pow(n,mod-2,mod);
		}
		
		//Returns index of highest number less than or equal to key
		 public static int upper(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key >= a[mid]) {
		                ans=mid;
		            	low = mid+1;
		            } else if(a[mid]>key){
		                high = mid - 1;
		            }
		        }
		        return ans;
		}
		
		//Returns index of least number greater than or equal to key
		 public static int lower(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key<=a[mid]) {
		                ans=mid;
		            	high = mid-1;
		            }
		            else{
		            		low=mid+1;
		            	}
		        }
		        return ans;
		} 
		   
		public long gcd(long r,long ans)
		{
			if(r==0) return ans;
			return gcd(ans%r,r);
		}
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String nextString() {
     		int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
	}	
}