Problem: Little Timofey has a big tree — an undirected connected graph with n vertices and no simple cycles. He likes to walk along it. His tree is flat so when he walks along it he sees it entirely. Quite naturally, when he stands on a vertex, he sees the tree as a rooted tree with the root in this vertex.

Timofey assumes that the more non-isomorphic subtrees are there in the tree, the more beautiful the tree is. A subtree of a vertex is a subgraph containing this vertex and all its descendants. You should tell Timofey the vertex in which he should stand to see the most beautiful rooted tree.

Subtrees of vertices u and v are isomorphic if the number of children of u equals the number of children of v, and their children can be arranged in such a way that the subtree of the first son of u is isomorphic to the subtree of the first son of v, the subtree of the second son of u is isomorphic to the subtree of the second son of v, and so on. In particular, subtrees consisting of single vertex are isomorphic to each other.

Input

First line contains single integer n (1 ≤ n ≤ 105) — number of vertices in the tree.

Each of the next n - 1 lines contains two integers ui and vi (1 ≤ ui, vi ≤ 105, ui ≠ vi), denoting the vertices the i-th edge connects.

It is guaranteed that the given graph is a tree.

Output

Print single integer — the index of the vertex in which Timofey should stand. If there are many answers, you can print any of them.

Examples

Input

3
1 2
2 3


Output

1


Input

7
1 2
4 2
2 3
5 6
6 7
3 7


Output

1


Input

10
1 7
1 8
9 4
5 1
9 2
3 5
10 6
10 9
5 10


Output

2

Note

In the first example we can stand in the vertex 1 or in the vertex 3 so that every subtree is non-isomorphic. If we stand in the vertex 2, then subtrees of vertices 1 and 3 are isomorphic.

In the second example, if we stand in the vertex 1, then only subtrees of vertices 4 and 5 are isomorphic.

In the third example, if we stand in the vertex 1, then subtrees of vertices 2, 3, 4, 6, 7 and 8 are isomorphic. If we stand in the vertex 2, than only subtrees of vertices 3, 4, 6, 7 and 8 are isomorphic. If we stand in the vertex 5, then subtrees of vertices 2, 3, 4, 6, 7 and 8 are isomorphic, and subtrees of vertices 1 and 9 are isomorphic as well: 
    
    
      
      1     9  
     /\    /\  
    7  8  4  2  
    

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.Random;
import java.util.ArrayList;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DTimofeyAndAFlatTree solver = new DTimofeyAndAFlatTree();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DTimofeyAndAFlatTree {
        Debug debug = new Debug(true);
        HashData[] hds;
        PartialHash[] phs;
        long mask = (1L << 32) - 1;
        int vertex = -1;
        int vertexVal = -1;
        LongHashMap map = new LongHashMap((int) 2e6, true);
        int nonZeroCnt = 0;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            Node[] nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
                nodes[i].id = i;
            }
            for (int i = 0; i < n - 1; i++) {
                Node a = nodes[in.readInt() - 1];
                Node b = nodes[in.readInt() - 1];
                a.adj.add(b);
                b.adj.add(a);
            }

            for (int i = 0; i < 1; i++) {
                hds = new HashData[]{new HashData((int) 1e5, (int) 1e9 + 7, RandomWrapper.INSTANCE.nextInt(3, (int) (1e9 + 6))), new HashData((int) 1e5, (int) 1e9 + 7, RandomWrapper.INSTANCE.nextInt(3, (int) (1e9 + 6)))};
                phs = new PartialHash[]{new PartialHash(hds[0]), new PartialHash(hds[1])};
                nonZeroCnt = 0;
                dfsForHash(nodes[0], null);
                dfsForVertex(nodes[0], null, 0);
            }


            debug.debug("vertexVal", vertexVal);
            out.println(vertex + 1);
        }

        public void update(int vertex) {
            if (nonZeroCnt > vertexVal) {
                vertexVal = nonZeroCnt;
                this.vertex = vertex;
            }
        }

        public void add(long x) {
            long val = map.get(x);
            map.put(x, val + 1);
            if (val == 0) {
                nonZeroCnt++;
            }
        }

        public void remove(long x) {
            long val = map.get(x);
            map.put(x, val - 1);
            if (val == 1) {
                nonZeroCnt--;
            }
        }

        public int hashWithout(int h, int i, int l, int r) {
            int left = phs[h].hash(l, i - 1, false);
            int right = phs[h].hash(i + 1, r, false);
            int leftSize = i - l;
            int rightSize = r - i;
            right = hds[h].mod.mul(right, hds[h].pow[leftSize]);
            int ans = hds[h].mod.plus(left, right);
            ans = hds[h].mod.plus(ans, hds[h].pow[leftSize + rightSize]);
            return ans;
        }

        public void dfsForHash(Node root, Node p) {
            root.hash = new LongArrayList(root.adj.size());
            for (Node node : root.adj) {
                if (node == p) {
                    continue;
                }
                dfsForHash(node, root);
                root.hash.add(node.hashVal);
            }
            root.hash.sort();
            phs[0].populate(i -> hds[0].hash(root.hash.get(i)), 0, root.hash.size() - 1);
            phs[1].populate(i -> hds[1].hash(root.hash.get(i)), 0, root.hash.size() - 1);
            for (PartialHash ph : phs) {
                root.hashVal = (root.hashVal << 32) | (ph.hash(0, root.hash.size() - 1, true) & mask);
            }
            add(root.hashVal);
        }

        public void dfsForVertex(Node root, Node p, long pHash) {
            if (p != null) {
                root.hash.add(pHash);
            }

            long original = root.hashVal;
            root.hash.sort();
            root.hashVal = 0;
            phs[0].populate(i -> hds[0].hash(root.hash.get(i)), 0, root.hash.size() - 1);
            phs[1].populate(i -> hds[1].hash(root.hash.get(i)), 0, root.hash.size() - 1);
            for (PartialHash ph : phs) {
                root.hashVal = (root.hashVal << 32) | (ph.hash(0, root.hash.size() - 1, true) & mask);
            }

            remove(original);
            add(root.hashVal);
            update(root.id);

            for (Node node : root.adj) {
                if (node == p) {
                    continue;
                }
                node.mark = 0;
                int index = root.hash.binarySearch(node.hashVal);
                for (int i = 0; i < 2; i++) {
                    node.mark = (node.mark << 32) | (hashWithout(i, index, 0, root.hash.size() - 1) & mask);
                }
            }

            remove(root.hashVal);
            for (Node node : root.adj) {
                if (node == p) {
                    continue;
                }
                add(node.mark);
                dfsForVertex(node, root, node.mark);
                remove(node.mark);
            }
            add(original);
        }

    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper(new Random());

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static interface LongEntryIterator {
        boolean hasNext();

        void next();

        long getEntryKey();

        long getEntryValue();

    }

    static class ExtGCD {
        public static int extGCD(int a, int b, int[] xy) {
            if (a >= b) {
                return extGCD0(a, b, xy);
            }
            int ans = extGCD0(b, a, xy);
            SequenceUtils.swap(xy, 0, 1);
            return ans;
        }

        private static int extGCD0(int a, int b, int[] xy) {
            if (b == 0) {
                xy[0] = 1;
                xy[1] = 0;
                return a;
            }
            int ans = extGCD0(b, a % b, xy);
            int x = xy[0];
            int y = xy[1];
            xy[0] = y;
            xy[1] = x - a / b * y;
            return ans;
        }

    }

    static interface InverseNumber {
    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Node {
        List<Node> adj = new ArrayList<>();
        LongArrayList hash;
        long hashVal;
        long mark;
        int id;

        public String toString() {
            return "" + (id + 1);
        }

    }

    static class Randomized {
        public static void shuffle(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, int x) {
            if (offline) {
                debug(name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf("%s=%s", name, x);
                out.println();
            }
            return this;
        }

    }

    static class LongHashMap {
        private int[] slot;
        private int[] next;
        private long[] keys;
        private long[] values;
        private int alloc;
        private boolean[] removed;
        private int mask;
        private int size;
        private boolean rehash;
        private Hasher hasher = new Hasher();

        public LongHashMap(int cap, boolean rehash) {
            this.mask = (1 << (32 - Integer.numberOfLeadingZeros(cap - 1))) - 1;
            slot = new int[mask + 1];
            next = new int[cap + 1];
            keys = new long[cap + 1];
            values = new long[cap + 1];
            removed = new boolean[cap + 1];
            this.rehash = rehash;
        }

        private void doubleCapacity() {
            int newSize = Math.max(next.length + 10, next.length * 2);
            next = Arrays.copyOf(next, newSize);
            keys = Arrays.copyOf(keys, newSize);
            values = Arrays.copyOf(values, newSize);
            removed = Arrays.copyOf(removed, newSize);
        }

        public void alloc() {
            alloc++;
            if (alloc >= next.length) {
                doubleCapacity();
            }
            next[alloc] = 0;
            removed[alloc] = false;
            size++;
        }

        private void rehash() {
            int[] newSlots = new int[Math.max(16, slot.length * 2)];
            int newMask = newSlots.length - 1;
            for (int i = 0; i < slot.length; i++) {
                if (slot[i] == 0) {
                    continue;
                }
                int head = slot[i];
                while (head != 0) {
                    int n = next[head];
                    int s = hash(keys[head]) & newMask;
                    next[head] = newSlots[s];
                    newSlots[s] = head;
                    head = n;
                }
            }
            this.slot = newSlots;
            this.mask = newMask;
        }

        private int hash(long x) {
            return hasher.hash(x);
        }

        public void put(long x, long y) {
            put(x, y, true);
        }

        public void put(long x, long y, boolean cover) {
            int h = hash(x);
            int s = h & mask;
            if (slot[s] == 0) {
                alloc();
                slot[s] = alloc;
                keys[alloc] = x;
                values[alloc] = y;
            } else {
                int index = findIndexOrLastEntry(s, x);
                if (keys[index] != x) {
                    alloc();
                    next[index] = alloc;
                    keys[alloc] = x;
                    values[alloc] = y;
                } else if (cover) {
                    values[index] = y;
                }
            }
            if (rehash && size >= slot.length) {
                rehash();
            }
        }

        public long getOrDefault(long x, long def) {
            int h = hash(x);
            int s = h & mask;
            if (slot[s] == 0) {
                return def;
            }
            int index = findIndexOrLastEntry(s, x);
            return keys[index] == x ? values[index] : def;
        }

        public long get(long x) {
            return getOrDefault(x, 0);
        }

        private int findIndexOrLastEntry(int s, long x) {
            int iter = slot[s];
            while (keys[iter] != x) {
                if (next[iter] != 0) {
                    iter = next[iter];
                } else {
                    return iter;
                }
            }
            return iter;
        }

        public LongEntryIterator iterator() {
            return new LongEntryIterator() {
                int index = 1;
                int readIndex = -1;


                public boolean hasNext() {
                    while (index <= alloc && removed[index]) {
                        index++;
                    }
                    return index <= alloc;
                }


                public long getEntryKey() {
                    return keys[readIndex];
                }


                public long getEntryValue() {
                    return values[readIndex];
                }


                public void next() {
                    if (!hasNext()) {
                        throw new IllegalStateException();
                    }
                    readIndex = index;
                    index++;
                }
            };
        }

        public String toString() {
            LongEntryIterator iterator = iterator();
            StringBuilder builder = new StringBuilder("{");
            while (iterator.hasNext()) {
                iterator.next();
                builder.append(iterator.getEntryKey()).append("->").append(iterator.getEntryValue()).append(',');
            }
            if (builder.charAt(builder.length() - 1) == ',') {
                builder.setLength(builder.length() - 1);
            }
            builder.append('}');
            return builder.toString();
        }

    }

    static class LongArrayList implements Cloneable {
        private int size;
        private int cap;
        private long[] data;
        private static final long[] EMPTY = new long[0];

        public LongArrayList(int cap) {
            this.cap = cap;
            if (cap == 0) {
                data = EMPTY;
            } else {
                data = new long[cap];
            }
        }

        public LongArrayList(LongArrayList list) {
            this.size = list.size;
            this.cap = list.cap;
            this.data = Arrays.copyOf(list.data, size);
        }

        public LongArrayList() {
            this(0);
        }

        public void ensureSpace(int req) {
            if (req > cap) {
                while (cap < req) {
                    cap = Math.max(cap + 10, 2 * cap);
                }
                data = Arrays.copyOf(data, cap);
            }
        }

        private void checkRange(int i) {
            if (i < 0 || i >= size) {
                throw new ArrayIndexOutOfBoundsException();
            }
        }

        public long get(int i) {
            checkRange(i);
            return data[i];
        }

        public void add(long x) {
            ensureSpace(size + 1);
            data[size++] = x;
        }

        public void addAll(long[] x, int offset, int len) {
            ensureSpace(size + len);
            System.arraycopy(x, offset, data, size, len);
            size += len;
        }

        public void addAll(LongArrayList list) {
            addAll(list.data, 0, list.size);
        }

        public void sort() {
            if (size <= 1) {
                return;
            }
            Randomized.shuffle(data, 0, size);
            Arrays.sort(data, 0, size);
        }

        public int binarySearch(long x) {
            return Arrays.binarySearch(data, 0, size, x);
        }

        public int size() {
            return size;
        }

        public long[] toArray() {
            return Arrays.copyOf(data, size);
        }

        public String toString() {
            return Arrays.toString(toArray());
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof LongArrayList)) {
                return false;
            }
            LongArrayList other = (LongArrayList) obj;
            return SequenceUtils.equal(data, 0, size - 1, other.data, 0, other.size - 1);
        }

        public int hashCode() {
            int h = 1;
            for (int i = 0; i < size; i++) {
                h = h * 31 + Long.hashCode(data[i]);
            }
            return h;
        }

        public LongArrayList clone() {
            LongArrayList ans = new LongArrayList();
            ans.addAll(this);
            return ans;
        }

    }

    static interface IntToIntegerFunction {
        int apply(int x);

    }

    static class SequenceUtils {
        public static void swap(int[] data, int i, int j) {
            int tmp = data[i];
            data[i] = data[j];
            data[j] = tmp;
        }

        public static boolean equal(long[] a, int al, int ar, long[] b, int bl, int br) {
            if ((ar - al) != (br - bl)) {
                return false;
            }
            for (int i = al, j = bl; i <= ar; i++, j++) {
                if (a[i] != b[j]) {
                    return false;
                }
            }
            return true;
        }

    }

    static class Modular {
        int m;

        public int getMod() {
            return m;
        }

        public Modular(int m) {
            this.m = m;
        }

        public Modular(long m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public Modular(double m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public String toString() {
            return "mod " + m;
        }

    }

    static class IntExtGCDObject {
        private int[] xy = new int[2];

        public int extgcd(int a, int b) {
            return ExtGCD.extGCD(a, b, xy);
        }

        public int getX() {
            return xy[0];
        }

    }

    static class Power implements InverseNumber {
        static IntExtGCDObject extGCD = new IntExtGCDObject();
        final Modular modular;

        public Power(Modular modular) {
            this.modular = modular;
        }

        public int inverse(int x) {
            int ans = inverseExtGCD(x);
//        if(modular.mul(ans, x) != 1){
//            throw new IllegalStateException();
//        }
            return ans;
        }

        public int inverseExtGCD(int x) {
            if (extGCD.extgcd(x, modular.getMod()) != 1) {
                throw new IllegalArgumentException();
            }
            return modular.valueOf(extGCD.getX());
        }

    }

    static class Hasher {
        private long time = System.nanoTime() + System.currentTimeMillis() * 31L;

        public int shuffle(long z) {
            z += time;
            z = (z ^ (z >>> 33)) * 0x62a9d9ed799705f5L;
            return (int) (((z ^ (z >>> 28)) * 0xcb24d0a5c88c35b3L) >>> 32);
        }

        public int hash(long x) {
            return shuffle(x);
        }

    }

    static class PartialHash {
        HashData hd;
        int[] hash;

        public PartialHash(HashData hd) {
            this.hd = hd;
            hash = new int[hd.pow.length];
        }

        public void populate(IntToIntegerFunction function, int l, int r) {
            if (l > r) {
                return;
            }
            if (l > 0) {
                hash[l - 1] = 0;
            }
            hash[l] = hd.mod.mul(function.apply(l), hd.pow[l]);
            for (int i = l + 1; i <= r; i++) {
                hash[i] = hd.mod.valueOf(hash[i - 1] + hd.pow[i] * (long) function.apply(i));
            }
        }

        public int hash(int l, int r, boolean verbose) {
            if (l > r) {
                return verbose ? hd.pow[0] : 0;
            }
            long h = hash[r];
            if (l > 0) {
                h -= hash[l - 1];
                h *= hd.inv[l];
            }
            if (verbose) {
                h += hd.pow[r - l + 1];
            }
            return hd.mod.valueOf(h);
        }

    }

    static class HashData {
        public Modular mod;
        public int[] inv;
        public int[] pow;

        public HashData(int n, int p, int x) {
            this.mod = new Modular(p);
            n = Math.max(n, 1);
            inv = new int[n + 1];
            pow = new int[n + 1];
            inv[0] = 1;
            pow[0] = 1;
            int invX = new Power(mod).inverse(x);
            for (int i = 1; i <= n; i++) {
                inv[i] = mod.mul(inv[i - 1], invX);
                pow[i] = mod.mul(pow[i - 1], x);
            }
        }

        public HashData(int n) {
            this(n, (int) 1e9 + 7, RandomWrapper.INSTANCE.nextInt(1, (int) 1e9 + 6));
        }

        public int hash(long x) {
            long high = x >>> 32;
            long low = x & ((1L << 32) - 1);
            return mod.valueOf(high * pow[1] + low);
        }

    }
}