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 javax.lang.model.util.ElementScanner6;

import java.io.*;

public class Main {

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();

    }





    static class Solver {

        class Node implements Comparable < Node > {
            int i;
            int cnt;

            Node(int i, int cnt) {
                this.i = i;
                this.cnt = cnt;
            }

            public int compareTo(Node n) {
                if (this.cnt == n.cnt) {
                    return Integer.compare(this.i, n.i);
                }
                return Integer.compare(this.cnt, n.cnt);
            }
        }

        public boolean done(int[] sp, int[] par) {
            int root;

            root = findSet(sp[0], par);

            for (int i = 1; i < sp.length; i++) {
                if (root != findSet(sp[i], par))
                    return false;
            }
            return true;
        }
        public int findSet(int i, int[] par) {
            int x = i;
            boolean flag = false;
            while (par[i] >= 0) {
                flag = true;
                i = par[i];
            }
            if (flag)
                par[x] = i;
            return i;
        }

        public void unionSet(int i, int j, int[] par) {
            int x = findSet(i, par);
            int y = findSet(j, par);
            if (x < y) {
                par[y] = x;
            } else {
                par[x] = y;
            }
        }

        public long pow(long a, long b, long MOD) {
            if (b == 0) {
                return 1;
            }
            if (b == 1) {
                return a;
            }
            long val = pow(a, b / 2, MOD);
            if (b % 2 == 0) {
                return val * val % MOD;
            } else {
                return val * (val * a % MOD) % MOD;

            }

        }


        public void minPrimeFactor(int n, int[] s) {
            boolean prime[] = new boolean[n + 1];
            Arrays.fill(prime, true);
            s[1] = 1;
            s[2] = 2;
            for (int i = 4; i <= n; i += 2) {
                prime[i] = false;
                s[i] = 2;
            }

            for (int i = 3; i <= n; i += 2) {
                if (prime[i]) {
                    s[i] = i;
                    for (int j = 2 * i; j <= n; j += i) {
                        prime[j] = false;
                        s[j] = i;
                    }
                }
            }

        }


        public void findAllPrime(int n, ArrayList < Node > al, int s[]) {
            int curr = s[n];
            int cnt = 1;
            while (n > 1) {
                n /= s[n];
                if (curr == s[n]) {
                    cnt++;
                    continue;

                }
                Node n1 = new Node(curr, cnt);
                al.add(n1);

                curr = s[n];
                cnt = 1;
            }
        }



        public int binarySearch(int n, int k) {
            int left = 1;
            int right = 100000000 + 5;
            int ans = 0;
            while (left <= right) {
                int mid = (left + right) / 2;
                if (n / mid >= k) {
                    left = mid + 1;
                    ans = mid;
                } else {
                    right = mid - 1;
                }
            }

            return ans;
        }
        public boolean checkPallindrom(String s) {
            char ch[] = s.toCharArray();

            for (int i = 0; i < s.length() / 2; i++) {
                if (ch[i] != ch[s.length() - 1 - i])
                    return false;
            }
            return true;
        }


        

        public void remove(ArrayList < Integer > [] al, int x) {
            for (int i = 0; i < al.length; i++) {
                for (int j = 0; j < al[i].size(); j++) {

                    if (al[i].get(j) == x)
                        al[i].remove(j);

                }
            }
        }

        public long gcd(long a, long b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }


        public void printDivisors(long n, ArrayList <Long> al) {
            // Note that this loop runs till square root 
            for (long i = 1; i <= Math.sqrt(n); i++) {
                if (n % i == 0) {
                    // If divisors are equal, print only one 
                    if (n / i == i) {
                        al.add(i);
                    } else // Otherwise print both 
                    {
                        al.add(i);
                        al.add(n / i);
                    }

                }
            }
        }

        public static long constructSegment(long seg[], long arr[], int low, int high, int pos) {
            if (low == high) {
                seg[pos] = arr[low];
                return seg[pos];
            }
            int mid = (low + high) / 2;
            long t1 = constructSegment(seg, arr, low, mid, (2 * pos) + 1);
            long t2 = constructSegment(seg, arr, mid + 1, high, (2 * pos) + 2);
            seg[pos] = t1 + t2;
            return seg[pos];

        }
        public static long querySegment(long seg[], int low, int high, int qlow, int qhigh, int pos) {

            if (qlow <= low && qhigh >= high) {
                return seg[pos];
            } else if (qlow > high || qhigh < low) {
                return 0;
            } else {
                long ans = 0;
                int mid = (low + high) / 2;
                ans += querySegment(seg, low, mid, qlow, qhigh, (2 * pos) + 1);
                ans += querySegment(seg, mid + 1, high, qlow, qhigh, (2 * pos) + 2);
                return ans;
            }

        }
        public static int lcs(char[] X, char[] Y, int m, int n) {
            if (m == 0 || n == 0)
                return 0;
            if (X[m - 1] == Y[n - 1])
                return 1 + lcs(X, Y, m - 1, n - 1);
            else
                return Integer.max(lcs(X, Y, m, n - 1), lcs(X, Y, m - 1, n));
        }

        public static long recursion(long start, long end, long cnt[], int a, int b) {

            long min = 0;
            long count = 0;
            int ans1 = -1;
            int ans2 = -1;
            int l = 0;
            int r = cnt.length - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (cnt[mid] >= start) {
                    ans1 = mid;
                    r = mid - 1;
                } else {
                    l = mid + 1;
                }
            }

            l = 0;
            r = cnt.length - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (cnt[mid] <= end) {
                    ans2 = mid;
                    l = mid + 1;
                } else {
                    r = mid - 1;
                }
            }

            if (ans1 == -1 || ans2 == -1 || ans2 < ans1) {
                // System.out.println("min1 "+min);
                min = a;
                return a;

            } else {
                min = b * (end - start + 1) * (ans2 - ans1 + 1);
            }
            if (start == end) {
                // System.out.println("min "+min);
                return min;
            }
            long mid = (end + start) / 2;
            min = Long.min(min, recursion(start, mid, cnt, a, b) + recursion(mid + 1, end, cnt, a, b));
            // System.out.println("min "+min);
            return min;
        }

        



        public int dfs_util(ArrayList < Integer > [] al, boolean vis[], int x,int[] s,int lvl[]) {

            vis[x] = true;
            int cnt=1;
            for (int i = 0; i < al[x].size(); i++) {

                if (!vis[al[x].get(i)]) {
                    lvl[al[x].get(i)]=lvl[x]+1;
                    cnt+=dfs_util(al, vis, al[x].get(i),s,lvl);
                    
                    
                    }


                }
                s[x] = cnt;
            return s[x];
        }

        public void dfs(ArrayList[] al,int[] s,int[] lvl) {

            boolean vis[] = new boolean[al.length];
            for (int i = 0; i < al.length; i++) {
                if (!vis[i]) {
                    lvl[i]=1;
                    dfs_util(al, vis, i,s,lvl);
                }
            }
        }




        private void solve(InputReader inp, PrintWriter out1) {

            int n = inp.nextInt();
            ArrayList<Integer> al[] = new ArrayList[n];
            
            for(int i=0;i<n;i++)
            {
                al[i]= new ArrayList<Integer>();
            }
            
            for(int i=0;i<n-1;i++)
            {
                int x1 = inp.nextInt();
                int x2 = inp.nextInt();
                al[x1-1].add(x2-1);
                al[x2-1].add(x1-1);
            }
            // System.out.println("hello"`);
            long ans[] = new long[n];
            Stack<Integer> s = new Stack<Integer>();
            int s1[] = new int[n];
            int lvl[] = new int[n];
            dfs(al,s1,lvl);
            // out1.println(Arrays.toString(lvl));
            // out1.println(Arrays.toString(s1));
            boolean vis[] = new boolean[n];
            s.clear();
            s.push(0);
            vis[0]=true;

            for(int i=0;i<n;i++)
            {
                ans[0]+=(long)lvl[i];
            }

            while(!s.isEmpty())
            {
                int x = s.pop();
                for(int i=0;i<al[x].size();i++)
                {
                    if(!vis[al[x].get(i)])
                    {
                        vis[al[x].get(i)]=true;
                        s.push(al[x].get(i));
                        ans[al[x].get(i)]=(long)ans[x]-(2*s1[al[x].get(i)])+n;
                    }
                }
               
            }
            Arrays.sort(ans);
            out1.println(ans[n-1]);
        }
    }





    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
class ele implements Comparable < ele > {
    int value;
    int i;
    boolean flag;
    public ele(int value, int i) {
        this.value = value;
        this.i = i;
        this.flag = false;
    }
    public int compareTo(ele e) {
        return Integer.compare(this.value, e.value);
    }
}