Vanya wants to minimize a tree. He can perform the following operation multiple times: choose a vertex v, and two disjoint (except for v) paths of equal length a0 = v, a1, ..., ak, and b0 = v, b1, ..., bk. Additionally, vertices a1, ..., ak, b1, ..., bk must not have any neighbours in the tree other than adjacent vertices of corresponding paths. After that, one of the paths may be merged into the other, that is, the vertices b1, ..., bk can be effectively erased:

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Help Vanya determine if it possible to make the tree into a path via a sequence of described operations, and if the answer is positive, also determine the shortest length of such path.

Input

The first line of input contains the number of vertices n (2 ≤ n ≤ 2·105).

Next n - 1 lines describe edges of the tree. Each of these lines contains two space-separated integers u and v (1 ≤ u, v ≤ n, u ≠ v) — indices of endpoints of the corresponding edge. It is guaranteed that the given graph is a tree.

Output

If it is impossible to obtain a path, print -1. Otherwise, print the minimum number of edges in a possible path.

Examples

Input

6
1 2
2 3
2 4
4 5
1 6


Output

3


Input

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


Output

-1

Note

In the first sample case, a path of three edges is obtained after merging paths 2 - 1 - 6 and 2 - 4 - 5.

It is impossible to perform any operation in the second sample case. For example, it is impossible to merge paths 1 - 3 - 4 and 1 - 5 - 6, since vertex 6 additionally has a neighbour 7 that is not present in the corresponding path.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.util.Collection;
import java.util.Scanner;
import java.util.Queue;
import java.util.ArrayDeque;
import java.util.TreeSet;
import java.util.ArrayList;

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

    static class TaskE {
        int n;
        Node[] nodes;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            n = in.nextInt();
            nodes = new Node[n + 10];
            for (int i = 1; i <= n; i++) {
                nodes[i] = new Node(i);
            }
            for (int i = 1; i < n; i++) {
                int a = in.nextInt(), b = in.nextInt();
                nodes[a].neighbour.add(b);
                nodes[b].neighbour.add(a);
            }
            int x = findFarthest(1);
            int y = findFarthest(x);
            int mid = findMid(x, y, new ArrayList<>());
            int ans = dfs(mid, mid, new boolean[n + 10]);
            while (ans % 2 == 0) ans /= 2;
            out.println(ans);
        }

        int dfs(int rt, int curr, boolean[] vis) {
            vis[curr] = true;
            if (rt != curr && nodes[curr].neighbour.size() == 1) return 0;
            TreeSet<Integer> depths = new TreeSet<>();
            for (int next : nodes[curr].neighbour) {
                if (vis[next]) continue;
                int ans = dfs(rt, next, vis);
                if (ans == -1) return -1;
                depths.add(ans + 1);
            }
            if (rt == curr) {
                if (depths.size() > 2) return -1;
                int sum = 0;
                for (int depth : depths) {
                    sum += depth;
                }
                return sum;
            } else {
                if (depths.size() > 1) return -1;
                else return depths.iterator().next();
            }
        }

        int findMid(int x, int y, ArrayList<Integer> path) {
            int len = path.size();
            if (x == y) {
                return path.get(len / 2);
            }
            path.add(x);
            for (int next : nodes[x].neighbour) {
                if (len > 0 && next == path.get(len - 1)) continue;
                int ans = findMid(next, y, path);
                if (ans != -1) return ans;
            }
            path.remove(len);
            return -1;
        }

        int findFarthest(int start) {
            boolean vis[] = new boolean[n + 10];
            Queue<Integer> q = new ArrayDeque<>();
            q.add(start);
            int latest = 0;
            while (!q.isEmpty()) {
                int curr = q.poll();
                if (vis[curr]) continue;
                vis[curr] = true;
                latest = curr;
                for (int next : nodes[curr].neighbour) {
                    q.add(next);
                }
            }
            return latest;
        }

        class Node {
            int id;
            ArrayList<Integer> neighbour = new ArrayList<>();

            public Node(int id) {
                this.id = id;
            }

        }

    }
}

