You have unweighted tree of n vertices. You have to assign a positive weight to each edge so that the following condition would hold:

  * For every two different leaves v_{1} and v_{2} of this tree, [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of weights of all edges on the simple path between v_{1} and v_{2} has to be equal to 0. 



Note that you can put very large positive integers (like 10^{(10^{10})}).

It's guaranteed that such assignment always exists under given constraints. Now let's define f as the number of distinct weights in assignment.

<image> In this example, assignment is valid, because bitwise XOR of all edge weights between every pair of leaves is 0. f value is 2 here, because there are 2 distinct edge weights(4 and 5).

<image> In this example, assignment is invalid, because bitwise XOR of all edge weights between vertex 1 and vertex 6 (3, 4, 5, 4) is not 0. 

What are the minimum and the maximum possible values of f for the given tree? Find and print both.

Input

The first line contains integer n (3 ≤ n ≤ 10^{5}) — the number of vertices in given tree.

The i-th of the next n-1 lines contains two integers a_{i} and b_{i} (1 ≤ a_{i} < b_{i} ≤ n) — it means there is an edge between a_{i} and b_{i}. It is guaranteed that given graph forms tree of n vertices.

Output

Print two integers — the minimum and maximum possible value of f can be made from valid assignment of given tree. Note that it's always possible to make an assignment under given constraints.

Examples

Input


6
1 3
2 3
3 4
4 5
5 6


Output


1 4


Input


6
1 3
2 3
3 4
4 5
4 6


Output


3 3


Input


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


Output


1 6

Note

In the first example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum. 

<image>

In the second example, possible assignments for each minimum and maximum are described in picture below. The f value of valid assignment of this tree is always 3. 

<image>

In the third example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum. 

<image>
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BEdgeWeightAssignment solver = new BEdgeWeightAssignment();
        solver.solve(1, in, out);
        out.close();
    }

    static class BEdgeWeightAssignment {
        int[][] G;
        boolean even;
        int[] parent;

        public void dfs(int node, int parent, int dist) {
            if (G[node].length == 1 && dist % 2 == 1) {
                even = false;
            }
            for (int i : G[node]) {
                if (i == parent) continue;
                dfs(i, node, dist + 1);
            }
        }

        public void dfs1(int node, int parent) {
            this.parent[node] = parent;
            for (int i : G[node]) {
                if (i == parent) continue;
                dfs1(i, node);
            }
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int[] from = new int[n - 1];
            int[] to = new int[n - 1];
            for (int i = 0; i < n - 1; i++) {
                from[i] = in.scanInt();
                to[i] = in.scanInt();
            }
            parent = new int[n + 1];
            G = CodeHash.packGraph(from, to, n);
            even = true;
            int ct = 0;
            {
                int leave = -1;
                for (int i = 1; i <= n; i++)
                    if (G[i].length == 1) {
                        leave = i;
                        ct++;
                    }
                dfs(leave, -1, 0);
            }
            int temp = 0;
            {
                int nonleave = -1;
                for (int i = 1; i <= n; i++) {
                    if (G[i].length != 1) {
                        nonleave = i;
                    }
                }
                dfs1(nonleave, -1);
                HashSet<Integer> set = new HashSet<>();
                for (int i = 1; i <= n; i++) {
                    if (G[i].length == 1 && !set.contains(parent[i])) {
                        set.add(parent[i]);
                        temp++;
                    }
                }
            }
            if (even) {
                out.println(1 + " " + (temp + (n - ct - 1)));
            } else {
                out.println(3 + " " + (temp + (n - ct - 1)));
            }
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }

    static class CodeHash {
        public static int[][] packGraph(int[] from, int[] to, int n) {
            return packGraph(from, to, n, from.length);
        }

        public static int[][] packGraph(int[] from, int[] to, int n, int m) {
            int[][] g = new int[n + 1][];
            int p[] = new int[n + 1];
            for (int i = 0; i < m; i++) p[from[i]]++;
            for (int i = 0; i < m; i++) p[to[i]]++;
            for (int i = 0; i <= n; i++) g[i] = new int[p[i]];
            for (int i = 0; i < m; i++) {
                g[from[i]][--p[from[i]]] = to[i];
                g[to[i]][--p[to[i]]] = from[i];
            }
            return g;
        }

    }
}

