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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cunbidun
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        ETreePainting solver = new ETreePainting();
        solver.solve(1, in, out);
        out.close();
    }

    static class ETreePainting {
        private InputReader in;
        private OutputWriter out;
        private ArrayList<Integer>[] tree;
        private long[] ans;
        private long[] preCal;
        private long[] size;
        private int n;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            this.in = in;
            this.out = out;
            n = in.nextInt();
            tree = in.nextTree(n);
            ans = new long[n + 1];
            size = new long[n + 1];
            preCal = new long[n + 1];
            dfs(1, 1);
            cal(1, 1);
            ans[1] = preCal[1];
            sol(1, 1);
            out.println(ArrayUtils.getMax(ans, 1, n));
        }

        private void sol(int u, int l) {
            for (int v : tree[u]) {
                if (v != l) {
                    ans[v] = ans[u] - 2 * size[v] + n;
                    sol(v, u);
                }
            }
        }

        private void dfs(int u, int l) {
            size[u] = 1;
            for (int v : tree[u]) {
                if (v != l) {
                    dfs(v, u);
                    size[u] += size[v];
                }
            }
        }

        private void cal(int u, int l) {
            preCal[u] = size[u];
            for (int v : tree[u]) {
                if (v != l) {
                    cal(v, u);
                    preCal[u] += preCal[v];
                }
            }
        }

    }

    static class InputReader extends InputStream {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        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 ArrayList<Integer>[] nextTree(int n) {
            ArrayList<Integer>[] tree = new ArrayList[n + 1];
            for (int i = 1; i <= n; i++) {
                tree[i] = new ArrayList<>();
            }
            for (int i = 1; i < n; i++) {
                int u = nextInt();
                int v = nextInt();
                tree[u].add(v);
                tree[v].add(u);
            }
            return tree;
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }

    static class MaxMin {
        public static <T extends Comparable<T>> T Max(T x, T y) {
            T max = x;
            if (y.compareTo(max) > 0) max = y;
            return max;
        }

    }

    static class ArrayUtils {
        public static long getMax(long[] array, int stIndex, int enIndex) {
            long max = array[stIndex];
            for (int i = stIndex; i <= enIndex; i++) {
                max = MaxMin.Max(max, array[i]);
            }
            return max;
        }

    }

    static class OutputWriter {
        private final PrintWriter out;

        public OutputWriter(OutputStream outputStream) {
            out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.out = new PrintWriter(writer);
        }

        public void close() {
            out.close();
        }

        public void println(long i) {
            out.println(i);
        }

    }
}

